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BEGIN:VEVENT
SUMMARY:Tsarev S.P (Siberian Federal University\, Krasnoyarsk\, Russia)
DTSTART:20200527T110000Z
DTEND:20200527T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/1
DESCRIPTION:Title: Discrete orthogonal polynomials: anomalies of time series and bound
ary effects of polynomial filters\nby Tsarev S.P (Siberian Federal Uni
versity\, Krasnoyarsk\, Russia) as part of Mathematical models and integra
tion methods\n\n\nAbstract\nWe describe a new result in the classical theo
ry of univariate discrete orthogonal polynomials: extremely fast decay of
their values near the interval boundary for polynomials of sufficiently hi
gh degree. This effect dramatically differs from the behavior of much more
popular in mathematical curricula continuous orthogonal polynomials.\n\nT
he practical importance of this new result for the theory of discrete poly
nomial filters (widely applied for detection of anomalies of time series o
f measurements) is demonstrated on the practical example of detection of o
utliers and small discontinuities in the publicly available GPS and GLONAS
S trajectories.\n\nDiscrete polynomial filters\, on one hand\, can detect
very small anomalies in sparse time series (with amplitude of order 10^(-1
1) relative to the typical values of the time series). On the other hand o
ur general result limits sensitivity of polynomial filters near the bounda
ry of the time series. The main problem in practical applications of the d
iscussed method is numerical instability of construction of the discrete o
rthogonal polynomials of high degree.\n\nZoom link for the talk: https://u
s04web.zoom.us/j/73902155099?pwd=ZnhXVUtIbUhPNmk4MFJ2dGpLNllZUT09\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.V. Meleshko\, N.P. Moshkin\, A.G. Petrova\, V.V. Pukhnachev
DTSTART:20200603T110000Z
DTEND:20200603T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/2
DESCRIPTION:Title: On exact analytical solutions of equations of Maxwell incompressibl
e viscoelastic medium\nby S.V. Meleshko\, N.P. Moshkin\, A.G. Petrova\
, V.V. Pukhnachev as part of Mathematical models and integration methods\n
\n\nAbstract\nUnstationary and stationary two-dimensional flows of incompr
essible viscoelastic Maxwell medium with upper\, low and corotational conv
ective derivatives in the theological constitutive law are considered. A c
lass of partially invariant solutions is analyzed. Using transition to Lag
rangian coordinates\, an exact solution of the problem of unsteady flow ne
ar free-stagnation point was constructed. For the model with Johnson-Segal
man convected derivative and special linear dependence of the vertical com
ponent of velocity\, the general solution was derived. Analysis of the ana
lytical unstationary solution provides a new class of stationary solutions
. The solutions found comprise both already known as well as substantially
new solutions. Nonsingular solutions of the stress tensor at the critical
point and bounded at infinity are constructed. Exact analytical formulae
for the stress tensor with the Weissenberg number Wi=1/2 are obtained.\n\n
Zoom link: https://us04web.zoom.us/j/75235003172?pwd=MXpVbGlLN0ZGQ1NpTVErV
2xvLzFBdz09\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karima Khusnutdinova (University Loughborough)
DTSTART:20200610T110000Z
DTEND:20200610T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/3
DESCRIPTION:Title: Near-integrable models for long surface and internal ring waves in
stratified shear flows\nby Karima Khusnutdinova (University Loughborou
gh) as part of Mathematical models and integration methods\n\n\nAbstract\n
In this talk I will first overview some general results concerning the eff
ects of the parallel shear flow on long weakly-nonlinear surface and inter
nal ring waves in a stratified fluid (e.g.\, oceanic internal waves genera
ted in narrow straits and river-sea interaction zones)\, generalising the
results for surface waves in a homogeneous fluid [1]. We showed that despi
te the clashing geometries of the waves and the shear flow\, there exists
a linear modal decomposition (separation of variables) in the far-field se
t of Euler equations describing the waves in a stratified fluid\, more com
plicated than the known decomposition for plane waves [2\,3]. We used it t
o describe the wavefronts of surface and internal waves\, and to derive a
2D cylindrical Korteweg - de Vries (cKdV)-type model for the amplitudes of
the waves. The distortion of the wavefronts is described explicitly by co
nstructing the singular solution (envelope of the general solution) of a r
espective nonlinear first-order differential equation. \n\nNext\, we consi
der a two-layer fluid with a rather general depth-dependent upper-layer cu
rrent (e.g. a river inflow\, or a wind-generated current). In the rigid-li
d approximation\, we find the necessary singular solution of the nonlinear
first-order ordinary differential equation responsible for the adjustment
of the speed of the long interfacial ring wave in different directions in
terms of the hypergeometric function [4]. This allows us to obtain an ana
lytical description of the wavefronts and vertical structure of the ring w
aves for a large family of the current profiles and to illustrate their de
pendence on the density jump and the type and the strength of the current
. We will also discuss a 2D generalisation of the long-wave instability cr
iterion for plane interfacial waves on a piecewise-constant current [4]\,
which on physical level manifests itself in the counter-intuitive squeezin
g of the wavefront of the interfacial ring wave.\n\nREFERENCES\n\n1. R.S.
Johnson\, Ring waves on the surface of shear flows: a linear and nonlinear
theory\, J. Fluid Mech.\, 215\, 1638-1660 (1990).\n\n2. K.R. Khusnutdinov
a\, X. Zhang\, Long ring waves in a stratified fluid over a shear flow\, J
. Fluid Mech.\, 794\, 17-44 (2016).\n\n3. K.R. Khusnutdinova\, X. Zhang\,
Nonlinear ring waves in a two-layer fluid\, Physica D\, 333\, 208-221 (201
6).\n\n4. K.R. Khusnutdinova\, Long internal ring waves in a two-layer flu
id with an upper-layer current\, submitted (2020). \n\n5. L.V. Ovsyannikov
\, Two-layer 'shallow water' model\, J. Appl. Math. Tech. Phys. 20\, 127-1
35 (1979).\n\nZoom limk: https://us04web.zoom.us/j/75476385312?pwd=dTU0U0V
QMTN5VlFOMVVHNmhaS1pCZz09\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey P. Tsarev (Siberian Federal University\, Krasnoyarsk\, Russ
ia)
DTSTART:20200617T110000Z
DTEND:20200617T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/4
DESCRIPTION:Title: Free interpolation of GLONASS/GPS orbits: solving a two-point bound
ary-value problem without solving differential equations\nby Sergey P.
Tsarev (Siberian Federal University\, Krasnoyarsk\, Russia) as part of Ma
thematical models and integration methods\n\n\nAbstract\nThis talk will gi
ve a totally different view to the problem addressed in my previous talk\n
\n"Discrete orthogonal polynomials: anomalies of time series and boundary
effects of polynomial filters". \n\nUsing a sort of adaptive filtering we
solve the problem of boundary attenuation effects of polynomial filters. T
he techniques we use may be classified as (elementary) machine learning.\n
\nAnother facet of the GNSS (Global Navigation Satellite Systems) theory a
nd practice exposed in this talk is the problem of interpolation of positi
ons of GNSS satellites.\nUsing the data from IGS (International GNSS Servi
ce) as an example\, we demonstrate a simple but unexpectedly effective tec
hnique that allows interpolation of the positions of GPS and GLONASS satel
lites with an accuracy of a few millimeters. It is natural to call the des
cribed interpolation technique "free" since it is not related to polynomia
ls\, nor trigonometric and other functions commonly used in standard inter
polation techniques.\n\nThe free interpolation technique also allows devel
oping much more accurate (nevertheless very simple) models of media that a
re important in the operation of space navigation systems: the ionosphere\
, troposphere\, etc.\n\nThe basis for the development of this method is Bi
g Data\, accumulated over many years of operation of satellite navigation
systems. We will discuss some common problems of the Big Data we use. The
following conclusion turned out to be paradoxical\, but real: the main pro
blem when working with big data is that there are too few of them...\n\nTh
is talk is a modified version of my Russian language talk given in 2018:\n
http://www.mathnet.ru/php/presentation.phtml?&presentid=24129&option_lang=
eng\n\nPaper references:\n\n1. Pustoshilov\, A. S.\, & Tsarev\, S. P. (201
7). Universal coefficients for precise interpolation of GNSS orbits from f
inal IGS SP3 data. In 2017 International Siberian Conference on Control an
d Communications (SIBCON) (pp. 1-6). IEEE. https://ieeexplore.ieee.org/abs
tract/document/7998463\n\n2. Pustoshilov\, A. S.\, & Tsarev\, S. P. (2018)
. Two-point free nonlinear interpolation of coordinates and velocities of
navigation satellites from SP3 data. (in Russian) Achievements of Modern R
adioelectronics / №12 - 2018 http://www.radiotec.ru/article/22602#englis
h\n\n3. Tsarev\, S. P.\, Denisenko\, V. V.\, & Valikhanov\, M. M. (2018).
Multidimensional free interpolation framework for high-precision modeling
of slant total electron contents in mid-latitude and equatorial regions. h
ttp://elib.sfu-kras.ru/handle/2311/109067?locale-attribute=en\n\nZoom link
: \nhttps://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQ
T09\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey V. Shmidt (Institute of Computational Modelling SB RAS\, Kr
asnoyarsk\, Russia)
DTSTART:20200624T110000Z
DTEND:20200624T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/5
DESCRIPTION:Title: On self-similar solutions for some problems of free turbulence\
nby Alexey V. Shmidt (Institute of Computational Modelling SB RAS\, Krasno
yarsk\, Russia) as part of Mathematical models and integration methods\n\n
\nAbstract\nThree-dimensional far turbulent wake in a passive stratified m
edium\,\naxisymmrtric submerged turbulent jet and far swirling turbulent w
ake are considered using RANS approach.\n\nWe use methods of a group-theor
etical analisys to reduce corresponding semi-emprirical models of turbulen
ce\nto systems of ordinary differential equations (ODEs). Modified shootin
g method and asymptotic expansion are used\n to solve boundary-value probl
ems for obtained systems of ODEs. The constructed solutions are in good ag
reement with\n experimental data. Moreover\, a detailed comparison with nu
merical solutions obtained by G.G. Chernykh with co-authors\n on the basis
of the full models of turbulence were conducted.\n\nKaptsov O.V.\, Shmidt
A.V. A three-dimensional semi-empirical model of a far turbulent wake //
J. Appl. Math. Mech.\, 2015\, V. 79\, № 5\, P. 459-466\n\nShmidt A.V. Se
lf-Similar solution of the problem of a turbulent flow in a round submerge
d jet // J. of Appl. Mech. and Tech. Phys.\, 2015\, V. 56\, № 3\, P. 414
-419\n\nShmidt A.V. Similarity in the far swirling momentumless turbulent
wake // J. SFU. Math. & Phys.\, 2020\, V. 13\, № 1\, P. 79-86\n\nНа о
снове подхода RANS рассмотрены трехмерный
дальний турбулентный след в пассивно-ст
ратифицированной среде\,\nосесимметричн
ая затопленная турбулентная струя и дал
ьний закрученный турбулентный след.\nС п
омощью методов теоретико-группового ана
лиза соответствующие полуэмпирические
модели турбулентности редуцируются\n к с
истемам обыкновенных дифференциальных
уравнений. Поставленные краевые задачи
для систем обыкновенных дифференциальн
ых\n уравнений решены с использованием м
одифицированного метода стрельбы и асим
птотического разложения решения\n в окре
стности особой точки. Построенные решен
ия находятся в хорошем согласии с экспер
иментальными данными.\n Кроме того\, было
проведено детальное сопоставление с чис
ленными решениями\, полученными Г.Г. Черн
ых с соавторами\n на основе полных моделе
й турбулентности.\n\nPlease join Zoom channel with your rea
l name!\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan G. Dimitrov (Institute of Nuclear Research and Nuclear Ener
getics (INRNE))
DTSTART:20200701T110000Z
DTEND:20200701T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/6
DESCRIPTION:Title: Applied General Theory of Relativity: Physical Principles of the Gl
obal Positioning System (GPS)\nby Bogdan G. Dimitrov (Institute of Nuc
lear Research and Nuclear Energetics (INRNE)) as part of Mathematical mode
ls and integration methods\n\n\nAbstract\n(The talk will be given in Russi
an with English slides)\n\nПрикладная Общая Теория О
тносительности: физические принципы Гло
бальной Системы Позиционирования (GPS)\n\nZo
om link:\nhttps://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3p
ZS0prQT09\n\nA general knowledge about the fundamental physical principles
of the Global Positioning System (GPS) will be presented. One of these pr
inciples is related to the fundamental fact (the Michelson-Morley experime
nt) about the independence of the velocity of light from the velocity of t
he source of light and the non-existence of “ether”\, which was the st
arting point for the creation of the Special Theory of Relativity by Alber
t Einstein. Particular attention will be paid to some (elementary) model e
xamples\, resulting in important relations\, concerning the frequency chan
ge of the signal between the stations on the Earth’s surface and the rot
ating satellites around the Earth. This frequency change depends on the ro
tation of the Earth\, as well as on the variation of the gravitational pot
ential. The amazing relation of these dependencies to the approach of Spec
ial Theory of Relativity will be demonstrated\, also the further extension
of the approach in the framework of the General Theory of Relativity\, wh
ich is being applied in the theory of the Global Positioning System since
2003.\n The Geocentric Relativistic Reference System will be briefly revi
ewed\, also the determination of the atomic clock times with respect to an
attached to the Earth rotating coordinate system\, which is important for
taking into account the General Relativity Theory effects during the sate
llite motion in the near-Earth space.\n \n REFERENCES\n1. Neil Ashby\,
Relativistic effects in the Global Positioning System\, in Gravitation an
d Relativity at the Turn of the Millenium\, Proceedings of the 15th Intern
ational Conference on General Relativity and Gravitation\, edited by N.Dad
hich and J. Narlikar (International University Centre for Astronomy and As
trophysics\, 1998).\n\n2. N. Ashby\, Relativity in the Global Positioning
System\, Living Reviews in Relativity 6\, 1-42 (2003)\, https://link.sprin
ger.com/content/pdf/10.12942%2Flrr-2003-1.pdf.\n\n3. N. Ashby\, and R. A.
Nelson\, in Relativity in Fundamental Astronomy: Dynamics\, Reference Fram
es\, and Data Analysis\, Proceedings of the IAU Symposium 261 2009\, edite
d by S. A. Klioner\, P. K. Seidelmann\, and M. H.Soffel (Cambridge Univers
ity Press\, Cambridge\, 2010).\n\n4. J. - F. Pascual Sanchez\, Introducing
Relativity in Global Navigation Satellite System\, Ann. Phys. (Leipzig) 1
6\, 258-273 (2007).\n\n5. Michael H. Soffel\, and Wen-Biao Han\, Applied G
eneral Relativity. Theory and Applications in Astronomy\, Celestial Mechan
ics and Metrology\, Springer Nature\, Switzerland AG 2019.\n\n6. Michael H
. Soffel\, and R. Langhans\, Space-Time Reference Systems (Springer-Verlag
\, Berlin Heidelberg\, 2013 ).\n\n7. Sergei M. Kopeikin\, Michael Efroimsk
y\, and George Kaplan\, Relativistic Celestial Mechanics of the Solar Syst
em (Wiley-VCH\, New York\, 2011).\n\n8. L. Duchayne\, Transfert de temps d
e haute performance: le Lien Micro-Onde de la mission ACES. Physique mathe
matique [math-ph]. PhD Thesis\, Observatoire de Paris\, 2008. Francais\, H
AL Id: tel-00349882\, https://tel.archives-ouvertes.fr/tel-00349882/docume
nt.\n\n9. M. Gulklett\, Relativistic effects in GPS and LEO\, October 8 20
03\, PhD Thesis\, University of Copenhagen\, Denmark\, Department of Geoph
ysics\, The Niels Bohr Institute for Physics\, Astronomy and Geophysics\,
available at https://www.yumpu.com/en/document/view/4706552/relativistic-e
_ects-in-gps-and-leo-niels-bohr-institutet.\n\n10. B. Hofmann-Wellenhof\,
and H. Moritz\, Physical Geodesy (Springer-Verlag\, Wien-New York\, 2005)
.\n\n11. Slava G. Turyshev\, Viktor T. Toth\, and Mikhail V. Sazhin\, Gene
ral relativistic observables of the GRAIL mission\, Phys. Rev. D87\, 02402
0 (2013)\, arXiv:1212.0232v4 [gr-qc].\n\n12. Slava G. Turyshev\, Mikhail V
. Sazhin\, and Viktor T. Toth\, General relativistic laser interferometric
observables of the GRACE-Follow-On mission\, Phys. Rev. D89\, 105029 (201
4)\, arXiv: 1402.7111v1 [qr-qc].\n\n13. Slava G. Turyshev\, Nan Yu\, and V
iktor T. Toth\, General relativistic observables for the ACES experiment\,
Phys. Rev. D93\, 045027 (2016)\, arXiv: 1512.09019v2 [gr-qc].\n\n14. R. A
. Nelson\, Relativistic time transfer in the vicinity of the Earth and in
the Solar system\, Metrologia 48\, S171 (2011).\n\n15. Bogdan G. Dimitrov\
, the (third) extended version of arXiv:1712.01101 [gr-qc] (contains a lot
of references).\n\n16. Bogdan G. Dimitrov\, New Mathematical Models of GP
S Intersatellite Communications in the Gravitational Field of the Near-Ear
th Space\, AIP Confer. Proc. 2075\, 040007 (2019)\; https://doi.org/10.106
3/1.5091167.\n\n\nБудут представлены некоторые
основные сведения о фундаментальных физ
ических принципах\, на которых основано
функционирование Глобальной Системы По
зиционирования (GPS). Один из этих принцип
ов имеет связь с фундаментальным фактом
о независимости скорости света от скоро
сти источника (эксперимент Майкельсона-
Морли) и несуществования т.н. «эфира»\, ко
торой являлся отправной точкой для пост
роении Специальной Теории Относительно
сти (СТО) Альбертом Эйнштейном. Особое вн
имание будет уделено некоторыми (элемен
тарными) модельными примерами\, на основ
е которых выводятся важные зависимости
о частотном изменении сигнала\, посылаем
ым станциями на Земле к спутникам (и обра
тно). Эта частота зависит от угловой скор
ости вращения Земли\, а также от изменени
я гравитационного потенциала. Будет про
демонстрировано удивительное согласова
ние этих зависимостей с подходами Специ
альной Теории Относительности\, а также
дальнейшее расширение подхода в рамках
Общей Теории Относительности (ОТО)\, кото
рая применяется в теории GPS после 2003-го г
ода.\n Коротко будет рассмотрена Геоцент
рическая Релятивистская Система Отсчет
а и определение времени атомных часов от
носительно вращающейся вместе со Землей
координатной системой. Время\, которое у
казывают эти часы\, существенно для иссл
едования эффектов ОТО при движении спут
ников в пространстве вокруг Земли.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan G. Dimitrov (Institute of Nuclear Research and Nuclear Ener
getics (INRNE))
DTSTART:20200708T110000Z
DTEND:20200708T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/7
DESCRIPTION:Title: Intersecting Null Cones and GPS\, GLONASS Intersatellite Communicat
ions in the Gravitational Field of Near-Earth Space with Account of Genera
l Relativity Theory\nby Bogdan G. Dimitrov (Institute of Nuclear Resea
rch and Nuclear Energetics (INRNE)) as part of Mathematical models and int
egration methods\n\n\nAbstract\n(The talk will be given in Russian with En
glish slides)\n\nZoom link: https://us04web.zoom.us/j/2084211239?pwd=bzZoZ
FF0RFl6TzBBZ2hHa3pZS0prQT09\n\nПересекающиеся нулевые
конусы межспутниковых коммуникаций для
GPS и GLONASS в гравитационном поле околозем
ного пространства с учетом эффектов Общ
ей Теории Относительности\n\nIn this report a theor
etical approach will be presented for intersatellite communications (ISC)
between two satellites (belonging to satellite configurations GPS or GLONA
SS)\, moving on (one-plane) elliptical orbits. The new approach is based o
n the introduction of two null cones with origins at the emitting-signal a
nd receiving-signal satellites. The two null cones (intersected also with
a hyperplane) account for the variable distance between the satellites. Th
is intersection of the two null cones gives the space-time interval in GRT
. Applying some theorems from higher algebra\, it was proved that this spa
ce-time distance can become zero\, consequently it can be also negative an
d positive. But in order to represent the geodesic distance travelled by t
he signal\, the space-time interval has to be "compatible" with the Euclid
ean distance. So this "compatibility condition"\, conditionally called "co
ndition for ISC"\, is the most important consequence of the theory. The ot
her important consequence is that the geodesic distance turns out to be th
e space-time interval\, but with account also of the "condition for ISC".
The geodesic distance turns out to be greater than the Euclidean distance
- a result\, entirely based on the "two null cones approach" and moreover\
, without any use of the Shapiro delay formulae. Application of the same h
igher algebra theorems shows that the geodesic distance cannot have any ze
roes\, in accord with being greater than the Euclidean distance. The theor
y also puts a restriction on the eccentric anomaly angle E=45.00251 [deg]\
, which is surprisingly close to the angle of disposition of the satellite
s in the GLONASS satellite constellation - 8 satellites within one and the
same plane equally spaced at 45 deg. Under some specific restrictions and
for the case of plane motion of the satellites\, an analytical formula wa
s derived for the propagation time of the signal\, emitted by a moving alo
ng an elliptical orbit satellite. The formula can be represented as a sum
of elliptic integrals of the first\, second and the third kind. \n\nRefere
nces\n\n1. Bogdan G. Dimitrov\, Two null gravitational cones in the theory
of GPS-intersatellite communications between two moving satellites. I. Ph
ysical and mathematical theory of the space-time interval and the geodesic
distance on intersecting null cones\, (third) extended version of https:/
/arxiv.org/abs/1712.01101v3 [gr-qc]\, 162 pages .\n\n2. Bogdan G. Dimitrov
\, New Mathematical Models of GPS Intersatellite Communications in the Gra
vitational Field of the Near-Earth Space\, AIP Confer. Proc. 2075\, 040007
(2019)\; https://doi.org/10.1063/1.5091167 \, 9 pages. \n\nВ этом д
окладе будет представлен теоретический
подход для спутниковых коммуникаций меж
ду двумя спутниками (GPS\, GLONASS)\, которые дв
игаются по эллиптических орбитах. Подхо
д основан на введении двух нулевых конус
ов с вершинами в спутниках\, посылающие и
принимающие сигналы соответственно. Дв
а нулевых конуса (пересекающихся также с
гиперплоскостью) учитывают изменяющеес
я расстояние между спутниками. Пересече
ние двух нулевых конусов задает простра
нственно-временной интервал в ОТО. Приме
няя некоторые теоремы из высшей алгебро
й\, было показано\, что пространственно-в
ременной интервал может равняться нулю\,
следовательно он может быть также и отр
ицательным\, и положительным. Но чтобы эт
от интервал представлял геодезическое р
асстояние\, пространственно-временной и
нтервал должен быть «согласованным» со
Евклидовым расстоянием. Таким образом\,
это «условие согласованности»\, условно
названное «условие для спутниковых комм
уникаций»\, является наиболее важным сле
дствием теории. Другое важное следствие:
геодезическое расстояние оказывается п
ространственно-временным интервалом\, н
о с учетом «условия для спутниковых комм
уникаций». Таким образом\, геодезическое
расстояние оказывается большим\, чем Ев
клидово расстояние – результат\, которо
й основывается только на «подходе двух к
онусов» и более того\, без использования
формулы Шапиро для замедления сигнала. П
рименение этих же теорем из высшей алгеб
рой показывает\, что геодезическое расст
ояние не имеет никаких нулей\, в соответс
твии с тем\, что оно больше евклидова рас
стояния. Теория также накладывает огран
ичение на угол эксцентричной аномалии E=4
5.00251 [deg]\, что удивительно близко к углово
му расстоянию спутников в конфигурации
ГЛОНАСС (российский аналог американског
о GPS) - 8 спутников в одной и той же плоскос
ти с равным интервалом в 45 градусов. При
некоторых конкретных ограничениях и для
случая плоского движения спутников\, ан
алитическая формула была получена для в
ремени распространения сигнала\, излуча
емым движущимся по эллиптической орбите
спутником. Формула может быть представл
ена в виде суммы эллиптических интеграл
ов первого\, второго и третьего рода.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shlapunov (Siberian Federal University\, Krasnoyarsk\, R
ussia)
DTSTART:20201009T110000Z
DTEND:20201009T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/8
DESCRIPTION:Title: Existence Theorems for Regular Spatially Periodic Solutions to the
Navier–Stokes Equations in R^3\nby Alexander Shlapunov (Siberian Fed
eral University\, Krasnoyarsk\, Russia) as part of Mathematical models and
integration methods\n\n\nAbstract\nWe consider the initial problem for th
e Navier–Stokes equations over ${\\mathbb R}^3 \\times [0\,T]$ with a po
sitive time $T$ in the spatially periodic setting. Identifying periodic ve
ctor-valued functions on ${\\mathbb R}^3$ with functions on the $3\\\,$-di
mensional torus ${\\mathbb T}^3$\, we prove that the problem induces an op
en both injective and surjective mapping of specially constructed scale of
function spaces of Bochner–Sobolev type parametrised with the smoothnes
s index $s\\in \\mathbb{N}$. The intersection of these classes with respec
t $s$ gives a uniqueness and existence theorem for smooth solutions to the
Navier–Stokes equations for each finite $T>0$. Then additional intersec
tion with respect to $T\\in (0\, +\\infty)$ leads to a uniqueness and exis
tence theorem for smooth solutions and data having prescribed asymptotic b
ehaviour at the infinity with respect to the time variable. Actually\, we
propose the following modified scheme of the proof of the existence theore
m\, based on apriori estimates and operator approach in Banach spaces:\n\n
1. We prove that the Navier–Stokes equations induce continuous injective
OPEN mapping between the chosen Banach spaces.\n\n2. Next\, the standard
topological arguments immediately imply that a nonempty open connected set
in a topological vector space coincides with the space itself if and only
if the set is closed. This reduces the proof of the existence theorem to
an $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a priori
estimate for the INVERSE IMAGE OF PRECOMPACT SETS in the target Banach spa
ce where $\\mathfrak{s}$\, $\\mathfrak{r}$ are Ladyzhenskaya–Prodi–Ser
rin numbers satisfying $2/\\mathfrak{s} + 3/\\mathfrak{r} = 1$ and $\\math
frak{r} > 3$. In this way we avoid proving a GLOBAL $L^\\mathfrak{s} ([0\,
T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a priori estimate.\n\n3. To prove
the weak $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a p
riori estimate with $\\mathfrak{r} > 3$ we calculate precisely the excess
between the left hand side and the right hand side of the corresponding en
ergy inequality\, that equals to $2r$ when expressed in terms of the Lebes
gue integrability index $r$. Then we operate with absolutely convergent se
ries involving Lebesgue norms that gives the possibility to group together
summands in a suitable way\, using the energy type inequalities\, interpo
lation inequalities and matching the asymptotic behaviour in order to excl
ude the unbounded sequences in the inverse image of a precompact set.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg V. Kaptsov (Institute of Computational Modeling SB RAS)
DTSTART:20201023T110000Z
DTEND:20201023T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/9
DESCRIPTION:Title: Exact Solution of Boussinesq equations for propagation of nonlinear
waves\nby Oleg V. Kaptsov (Institute of Computational Modeling SB RAS
) as part of Mathematical models and integration methods\n\n\nAbstract\nIn
this paper\, we consider two Boussinesq models that describe propagation
of small-amplitude long water waves. Exact solutions of the classical Bous
sinesq equation that represent the interaction of wave packets and waves o
n solitons are found. We use the Hirota representation and computer algebr
a methods. Moreover\, we find various solutions for one of the variants of
the Boussinesq system. In particular\, these solutions can be interpreted
as the fusion and decay of solitary waves\, as well as the interaction of
more complex structures.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg V. Kaptsov (Institute of Computational Modeling SB RAS)
DTSTART:20201106T110000Z
DTEND:20201106T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/10
DESCRIPTION:Title: Iterations and groups of formal transformations\nby Oleg V. Ka
ptsov (Institute of Computational Modeling SB RAS) as part of Mathematical
models and integration methods\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. Е. Миронов (Институт математики им
. С. Л. Соболева СО РАН)
DTSTART:20201113T110000Z
DTEND:20201113T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/11
DESCRIPTION:Title: Интегрируемые магнитные геодезичес
кие потоки на двумерном торе и системы г
идродинамического типа\nby А. Е. Миронов
(Институт математики им. С. Л. Соболева С
О РАН) as part of Mathematical models and integration methods\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. Е. Миронов (Институт математики им
. С. Л. Соболева СО РАН)
DTSTART:20201127T110000Z
DTEND:20201127T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/12
DESCRIPTION:Title: Коммутирующие разностные операторы
\nby А. Е. Миронов (Институт математики и
м. С. Л. Соболева СО РАН) as part of Mathematical models a
nd integration methods\n\n\nAbstract\nВ докладе будет рас
сказано о задаче построения коммутативн
ых колец разностных операторов. С помощь
ю одноточечных коммутирующих разностны
х операторов ранга один будет построена
дискретизация оператора Ламе.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. I. Kaptsov (Keldysh Institute of Applied Mathematics of Russian
Academy of Science)
DTSTART:20201211T110000Z
DTEND:20201211T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/13
DESCRIPTION:Title: Invariant finite-difference schemes for equations of continuous me
dium possessing finite-difference conservation laws\nby E. I. Kaptsov
(Keldysh Institute of Applied Mathematics of Russian Academy of Science) a
s part of Mathematical models and integration methods\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shlapunov (Siberian Federal University\, Krasnoyarsk\, R
ussia)
DTSTART:20201225T110000Z
DTEND:20201225T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/14
DESCRIPTION:Title: Existence theorems for regular solutions to the Cauchy problem for
the Navier-Stokes equations in R^3\nby Alexander Shlapunov (Siberian
Federal University\, Krasnoyarsk\, Russia) as part of Mathematical models
and integration methods\n\n\nAbstract\nWe consider the Cauchy problem for
the Navier-Stokes equations over ${\\mathbb R}^3 \\times [0\,T]$ with a po
sitive time $T$ over a specially constructed scale of function spaces of B
ochner-Sobolev type. We prove that the problem induces an open both inject
ive and surjective mapping of each space of the scale. In particular\, int
ersection of these classes gives a uniqueness and existence theorem for sm
ooth solutions to the Navier-Stokes equations for smooth data with a presc
ribed asymptotic behaviour at the infinity with respect to the time and th
e space variables. Actually\, we propose the following modified scheme of
the proof of the existence theorem\, based on apriori estimates and operat
or approach in Banach spaces:\n\n1. We prove that the Navier-Stokes equati
ons induce continuous injective OPEN mapping between the chosen Banach spa
ces.\n\n2. Next\, the standard topological arguments immediately imply tha
t a nonempty open connected set in a topological vector space coincides wi
th the space itself if and only if the set is closed. This reduces the pro
of of the existence theorem to an $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{
r} ({\\mathbb R^3}))$ a priori estimate for the INVERSE IMAGE OF PRECOMPAC
T SETS in the target Banach space where $\\mathfrak{s}$\, $\\mathfrak{s}$
are Ladyzhenskaya-Prodi-Serrin numbers satisfying $2/\\mathfrak{s} + 3/\\m
athfrak{r} = 1$ and $\\mathfrak{r} > 3$. In this way we avoid proving a GL
OBAL $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a prior
i estimate.\n\n3. To prove the weak $L^\\mathfrak{s} ([0\,T]\, L^\\mathfra
k{r} ({\\mathbb R^3}))$ a priori estimate with $\\mathfrak{r} > 3$ we calc
ulate precisely the excess between the left hand side and the right hand s
ide of the corresponding energy inequality\, that equals to $2r$ when expr
essed in terms of the Lebesgue integrability index $r$. Then we operate wi
th absolutely convergent series involving Lebesgue norms that gives the po
ssibility to group together summands in a suitable way\, using the energy
type inequalities\, interpolation inequalities and matching the asymptotic
behaviour in order to exclude the unbounded sequences in the inverse imag
e of a precompact set.\n\nAn early version of the paper is uploaded on arx
iv.org: https://arxiv.org/abs/2009.10530\nA similar approach can be used f
or investigation of the Navier-Stokes equations in the periodic setting: h
ttps://arxiv.org/abs/2007.14911\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.N. Rogalev (Institute of Computational Modeling SB RAS)
DTSTART:20210204T110000Z
DTEND:20210204T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/15
DESCRIPTION:Title: Regularization of numerical estimation of the sets of solutions of
ODEs in stability problems on a finite time interval\nby A.N. Rogale
v (Institute of Computational Modeling SB RAS) as part of Mathematical mod
els and integration methods\n\n\nAbstract\nThe sets of ODE solutions\, wit
h initial data belonging to the initial data regions\, have complex bounda
ries (boundary surfaces in the dimension space). For the boundaries of the
sets of solutions (surfaces in the space of solutions)\, it is impossible
to choose formulas of functions with the help of which it was possible to
describe the boundaries. As a result\, there are two possibilities — ei
ther to describe the values of the boundary surfaces in a set of discrete
points (on a grid)\, or to calculate their estimates of the maximum values
in the directions of the coordinate axes\, or the maximum in any chosen d
irection. The paper investigates and further uses the injectivity property
of solutions to ODEs. For linear systems of ODEs the shift operator is l
inear and monomorphic (i.e.\, injective). These properties are also posses
sed by the resolving operator\, which associates with the initial value th
e solution of the corresponding Cauchy problem (the entire solution\, not
its value at a point) as an element of space.\n\nFor nonlinear ODE systems
that have unique solutions in a certain region of initial data\, the boun
daries of the regions of initial data pass into the boundaries of the regi
ons of solutions at each specific moment in time. The class of such nonlin
ear ODE systems consists of systems whose solutions are uniformly bounded
(Lagrange stable). Preliminarily\, it is useful to construct a regularizat
ion of estimates for the boundaries of the solution sets\, passing to the
linear approximation of the original system. Regularization is understood
as finding information about sets of exact solutions. This regularization
establishes the values of compression / expansion in the given directions
\, offset along the time axis\, and rotation through some angle. Examples
of stability studies on a finite time interval are given.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Aksenov
DTSTART:20210218T110000Z
DTEND:20210218T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/16
DESCRIPTION:Title: Symmetries\, conservation laws\, and exact solutions to a one-dime
nsional system of shallow water equations over an uneven bottom\nby A.
V. Aksenov as part of Mathematical models and integration methods\n\n\nAbs
tract\nThe symmetries of a one-dimensional system of shallow water equatio
ns over an uneven bottom in Euler’s variables are classified. Based on t
he results of the group classification obtained\, it is concluded that it
is possible to reduce the one-dimensional system of shallow water equation
s to a linear system of equations using point transformations only in the
cases of horizontal and inclined bottom profiles. We also classify the con
tact symmetries of the one-dimensional shallow water equation over an unev
en bottom in Lagrangian’s variables.\n\nThe hydrodynamic conservation la
ws of a one-dimensional system of shallow water equations in Eulerian’s
variables are classified. A new basic conservation law is obtained. The fi
rst-order conservation laws of the one-dimensional shallow water equation
in Lagrangian’s variables are classified.\n\nA three-parameter family of
exact solutions of a one-dimensional system of shallow water equations ov
er an inclined bottom is obtained and investigated\, describing the ”ste
p’’ wave's arrival on the shore and its reflection from it. The nonlin
ear the overwash effect and the effect of the amplification of the incomin
g wave when it is reflected from the shore are described.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Stepanyants (School of Sciences\, University of Southern Quee
nsland\, Toowoomba\, Australia)
DTSTART:20210311T110000Z
DTEND:20210311T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/17
DESCRIPTION:Title: The asymptotic approach to the description of two-dimensional soli
ton patterns in the oceans\nby Yury Stepanyants (School of Sciences\,
University of Southern Queensland\, Toowoomba\, Australia) as part of Math
ematical models and integration methods\n\n\nAbstract\nThe asymptotic appr
oach is suggested for the description of interacting surface and internal
oceanic solitary waves. This approach allows one to describe a stationary
moving wave patterns consisting of two plane solitary waves moving at an a
ngle to each other. The results obtained within the approximate asymptotic
theory is validated by comparison with the exact two-soliton solution of
the Kadomtsev–Petviashvili equation. The suggested approach is equally a
pplicable to a wide class of non-integrable equations too. As an example\,
the asymptotic theory is applied to the description of wave patterns in t
he 2D Benjamin–Ono equation describing internal waves in the infinitely
deep ocean containing a relatively thin one of the layers.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Юрий Шанько (Институт вычислительно
го моделирования СО РАН)
DTSTART:20210325T110000Z
DTEND:20210325T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/18
DESCRIPTION:Title: Решение задачи Л.В. Овсянникова о дв
умерных изотермических движениях полит
ропного газа\nby Юрий Шанько (Институт в
ычислительного моделирования СО РАН) as pa
rt of Mathematical models and integration methods\n\n\nAbstract\nВ док
ладе исследуется переопределенная сист
ема уравнений в частных производных\n\n$u_t
+ uu_x + vu_y + p_x = 0$\,\n\n$v_t + uv_x + vv_y + p_y = 0$\,\n\n$u_x + v
_y = 0\,$ $\\qquad$ $\\qquad$ $\\quad$ (1)\n\n$p_t + up_x + vp_y = 0$\
,\n\nявляющаяся двумерным аналогом общей
трехмерной системы\,\nзадача исследовани
я на совместность которой была поставле
на\nв статье Л.В. Овсянникова «О "простых"
решениях уравнений динамики политропно
го газа».\nСистема (1) описывает так назыв
аемые тепловые (с постоянной плотностью)
движения политропного газа.\nК этой же с
истеме сводятся изотермические (с посто
янной скоростью звука) движения газа при
показателе адиабаты не равном $1$.\nВ гидр
одинамике данная система задает двумерн
ые движения жидкости с дополнительным у
словием постоянства давления в частице.\
nЭто условие позволяет интерпретировать
каждое ее решение\, как движение жидкост
и со свободной границей.\nСистема (1) прив
едена к пассивному виду и полностью прои
нтегрирована.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:О. В. Капцов (Институт вычислительно
го моделирования СО РАН)
DTSTART:20210408T110000Z
DTEND:20210408T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/19
DESCRIPTION:Title: Общие решения некоторых линейных во
лновых уравнений с переменными коэффиц
иентами\nby О. В. Капцов (Институт вычисл
ительного моделирования СО РАН) as part of Math
ematical models and integration methods\n\n\nAbstract\nВ работе н
айдены общие решения для некоторых клас
сов линейных волновых уравнений с перем
енными коэффициентами. Такие уравнения
описывают колебания стержней\, акустиче
ские волны\, а также к ним сводятся некот
орые модели газовой динамики. Для постро
ения решений используются преобразован
ия типа Леви\, которые являются дифферен
циальными подстановками первого порядк
а и их итерациями. Приводятся конкретные
примеры общих решений\, зависящих от про
изводных произвольных функций.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.V. Meleshko
DTSTART:20210415T110000Z
DTEND:20210415T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/20
DESCRIPTION:Title: On generalized simple waves in continuum mechanics\nby S.V. Me
leshko as part of Mathematical models and integration methods\n\n\nAbstrac
t\nOne of the well-known classes of solutions of many models of continuum
mechanics is a set of solutions called simple wave-type solutions. From th
e method of differential constraints point of view\, this class of solutio
ns is described by homogeneous differential constraints. Application of t
he method of differential constraints allows one to generalize this class.
The main feature of this class of solutions is that finding a solution of
the original system of equations is reduced to solving a system of ordina
ry differential equations. In particular\, the presentation will show that
finding a solution of any Cauchy problem of a homogeneous system of equat
ions written in Riemann invariants\, admitting a differential constraint\,
is reduced to solving the Cauchy problem of system of ordinary differenti
al equations. This is similar to the method of characteristics for a parti
al differential equation with a single dependent variable. Illustrations o
f solutions for some initial data are given. Several models will be demons
trated in the presentation.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:С.В. Хабиров
DTSTART:20210422T110000Z
DTEND:20210422T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/21
DESCRIPTION:Title: Стационарная плоская вихревая подм
одель идеального газа\nby С.В. Хабиров as
part of Mathematical models and integration methods\n\n\nAbstract\nПод
модель идеального газа\, инвариантная от
носительно переносов по времени и по одн
ому пространственному направлению в слу
чае вихревых движений имеет 4 интеграла.
Для функции тока и удельного объема полу
чена система нелинейных дифференциальн
ых уравнений 3-го порядка с одним произво
льным элементом\, включающим в себя урав
нение состояния и произвольные функции
интегралов. Найдены преобразования экви
валентности по произвольному элементу.
Решена задача групповой классификации.
Получена оптимальная система неподобны
х подалгебр для алгебр из групповой клас
сификации. Рассмотрены примеры инвариан
тных решений\, описывающие вихревые движ
ения газа с переменной энтропией\, в том
числе точечный источник или сток. На дву
мерных подалгебрах получены аналоги про
стых волн.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Е.Н. Пелиновский (Институт прикладно
й физики РАН\, Нижний Новгород)
DTSTART:20210513T110000Z
DTEND:20210513T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/22
DESCRIPTION:Title: Бегущие волны в сильно неоднородных
средах\nby Е.Н. Пелиновский (Институт пр
икладной физики РАН\, Нижний Новгород) as p
art of Mathematical models and integration methods\n\n\nAbstract\nПод
распространяющейся волной в линейной те
ории обычно понимает функцию $f(x – ct)$ с п
роизвольной зависимостью от других прос
транственных координат (здесь $t$ — время
\, и $x$ — координата). Их нахождение в случ
ае одной пространственной координаты св
одится к решению в простейшем случае сис
темы обыкновенных дифференциальных ура
внений. Более сложно найти бегущие волны
в волноводах со сложной поперечной стру
ктурой\, и\, например\, нахождение бегущих
волн в жидкости со свободной поверхност
ью стало предметом специального раздела
нелинейной математики. Если параметры с
реды меняются медленно во времени или пл
авно в пространстве\, то волна локально о
писывается теми же выражениями\, что и в
однородной среде\, а изменение амплитуды
и фазы волны находится с помощью лучевы
х методов\, или более строго с помощью ас
имптотической процедуры. Уже давно было
отмечено\, что в некоторых случаях асимп
тотические решения являются точными и н
е требуют плавности изменения параметро
в среды. При этом возникают вопросы\, явл
яются ли такие решения бегущими волнами\
, если среда не является плавно неодноро
дной. В настоящем докладе эта проблема о
бсуждается применительно к волнам на во
де. Показывается\, что существуют нескол
ько профилей переменной глубины\, когда
асимптотические решения для линейных во
лн становятся точными решениями. Такие р
ешения всегда имеют сингулярные точки. Н
аряду с монохроматическими волнами\, пол
учены решения в виде бегущих импульсов\,
и исследована их форма. В частности\, для
одного класса донной геометрии поверхно
стная волна должна быть знакопеременной
\, при этом волна скорости частиц меняет
свою форму по мере распространения. Полу
чены соответствующие решения начальной
задачи\, демонстрирующие особенности фо
рмирования бегущих волн\, движущихся в п
ротивоположных направлениях\, при этом в
общем случае формируется зона переменн
ого течения между двумя разбегающими во
лнами. Эти решения применяются для изуче
ния трансформации и отражения волны от и
злома глубины. Несмотря на «точечность»
отражения\, форма отраженной и преломлен
ной волны меняется кардинально\, в частн
ости для любой формы падающей волны\, тра
нсформированная волна является знакопе
ременной. Приводятся примеры бегущих во
лн в атмосферной акустике\, солнечной ат
мосфере и физики внутренних волн в страт
ифицированной жидкости. Существенно мен
ьше результатов получено в нелинейной з
адаче.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.A. Talyshev
DTSTART:20210520T110000Z
DTEND:20210520T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/23
DESCRIPTION:Title: On the Lifetime of a Free Neutron\nby A.A. Talyshev as part of
Mathematical models and integration methods\n\n\nAbstract\nDetermination
of the lifetime of a free neutron by the beam method and the 'bottled' met
hod give aloud different values [1]\, [2]. And this difference has not yet
been explained by insufficient accuracy methods\, no relativistic correct
ion.\nIn the beam method neutrons move at a speed of about 10000 km/sec\,
and in the 'bottled' method is much slower. On the other hand\, we can con
structing coordinate transformations inertial frames of reference abandoni
ng the direct comparing moving and stationary objects and from the assumpt
ion about the finiteness of the speed of light [3]. These transformations
lead to the maximum speed. And with a certain agreement on the choice of b
ases coincide with the Lorentz transformations (if we take this limiting s
peed for the speed of light). In this case\, the correction for time dilat
ion does not have to coincide with the generally accepted in the special t
heory of relativity.\n\n1. A. T. Yue\, M. S. Dewey\, D. M. Gilliam\, G. L.
Greene\, A. B. Laptev\, J. S. Nico\, W. M. Snow\, and F. E. Wietfeldt Imp
roved Determination of the Neutron Lifetime // Phys. Rev. Lett. 2013. V. 1
11. P. 222501. arXiv:1309.2623v2 [nucl-ex] 27 Nov 2013.\n\n2. Серебр
ов А. П. Разногласие между методом хранен
ия ультрахолодных нейтронов и пучковым
методом при измерении времени жизни ней
трона\, УФН\, т. 189\, № 6\, с. 635–641.\n\n3. Talyshev A. A
. On the Geometric Approach to Transformations of the Coordinates of Inert
ial Frames of Reference\, 'Nonlinear Dynamics\, Chaos\, and Complexity'\,
Higher Education Press\, Springer\, 2021\, pp. 113–124.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov
DTSTART:20210916T110000Z
DTEND:20210916T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/24
DESCRIPTION:Title: Symmetries and solutions of the three-dimensional Kadomtsev — Pe
tviashvili equation\nby O. V. Kaptsov as part of Mathematical models a
nd integration methods\n\n\nAbstract\nA symmetry group of the three-dimens
ional Kadomtsev — Petviashvili equation is calculated. An example of an
invariant solution is given. Exact solutions for the equation under study
in the form of double waves are revealed. The resulting solutions are expr
essed in terms of elementary functions and describe an interaction between
a pair of solitons. Smooth bounded rational solutions are also constructe
d.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Tsarev (Siberian Federal University (Krasnoyarsk\, Russia))
DTSTART:20210930T110000Z
DTEND:20210930T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/25
DESCRIPTION:Title: Integration of algebraic functions\, polynomial approximation\, no
nclassical boundary problems and Poncelet-type theorems\nby Sergey Tsa
rev (Siberian Federal University (Krasnoyarsk\, Russia)) as part of Mathem
atical models and integration methods\n\n\nAbstract\nIn this review talk w
e expose remarkably tight relations between the four topics mentioned in t
he title. Starting from the paper by N. H. Abel published in 1826 and subs
equent results of Chebyshev and Zolotarev we finish at the recent results
by Burskii\, Zhedanov\, Malyshev (et al.) devoted to algorithmic decidabi
lity of some identities for the values of the Weierstrass P-function\, une
xpected elementary geometric applications and many\, many more hidden equi
valences in seemingly unrelated areas of analysis\, modern computer algebr
a and geometry.\n \nThis talk will be given in Russian\, the English versi
on was presented on 16-09-2021 at Beijing-Novosibirsk seminar on geometry
and mathematical physics ( http://english.math.pku.edu.cn/conferences/244.
html ). The video and slides of that talk can be found at https://cloud.ma
il.ru/public/S4Pp/wJ5iFcggM\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay N. Osipov (Krasnoyarsk Mathematical Center)
DTSTART:20211014T110000Z
DTEND:20211014T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/26
DESCRIPTION:Title: Simplification of Nested Real Radicals Revisited\nby Nikolay N
. Osipov (Krasnoyarsk Mathematical Center) as part of Mathematical models
and integration methods\n\n\nAbstract\nThe problem of simplification of ne
sted radicals over arbitrary number fields was studied by many authors. Th
e case of real radicals over real number fields is somewhat easier to stud
y (at least\, from theoretical point of view). In particular\, an efficien
t (i.e.\, a polynomial-time) algorithm of simplification of at most doubly
nested real radicals is known. However\, this algorithm does not guarante
e complete simplification for the case of radicals with nesting depth more
than two. In the talk\, we give a detailed presentation of the theory tha
t provides an algorithm which simplifies triply nested reals radicals over
the field of rationals. Some new examples of triply (or more) nested real
radicals that cannot be simplified are also given.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Zakharov
DTSTART:20211020T120000Z
DTEND:20211020T130000Z
DTSTAMP:20260404T111326Z
UID:mmandim/27
DESCRIPTION:Title: Lumps and lump chain solutions of the KP-I equation\nby Dmitry
Zakharov as part of Mathematical models and integration methods\n\n\nAbst
ract\nThe Kadomstev—Petviashvili equation is one of the fundamental equa
tions in the theory of integrable systems. The KP equation comes in two ph
ysically distinct forms: KP-I and KP-II. The KP-I equation has a large fam
ily of rational solutions known as lumps. A single lump is a spatially loc
alized soliton\, and lumps can scatter on one another or form bound states
. The KP-II equation does not have any spatially localized solutions\, but
has a rich family of line soliton solutions.\n\nI will discuss two new fa
milies of solutions of the KP-I equation\, obtained using the Grammian for
m of the tau-function. The first is the family of lump chain solutions. A
single lump chain consists of a linear arrangement of lumps\, similar to a
line soliton of KP-II. More generally\, lump chains can form evolving pol
ygonal arrangements whose structure closely resembles that of the line sol
iton solutions of KP-II. I will also show how lump chains and line soliton
s may absorb\, emit\, and reabsorb individual lumps.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Pavlov (Lebedev Physical Institute RAS\, Moscow)
DTSTART:20211028T110000Z
DTEND:20211028T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/28
DESCRIPTION:Title: Non-diagonalisable Hydrodynamic Type Systems\, Integrable by Tsare
v's Generalised Hodograph Method\nby Maxim Pavlov (Lebedev Physical In
stitute RAS\, Moscow) as part of Mathematical models and integration metho
ds\n\n\nAbstract\nWe present a wide class of non-diagonalizable hydrodynam
ic type systems\, which can be integrated by Tsarev's generalized hodograp
h method. This class of hydrodynamic type systems contains Jordan blocks 2
x2 only. The Haantjes tensor has vanished. This means such 2N component hy
drodynamic type systems possess N Riemann invariants and N double eigenval
ues only.\n\nFirst multi-component example was extracted from El's nonloca
l kinetic equation\, describing dense soliton gas. All conservation laws a
nd commuting flows were found. A general solution is constructed.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. I. Tribelsky (Faculty of Physics\, M. V. Lomonosov Moscow State
University)
DTSTART:20211111T110000Z
DTEND:20211111T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/29
DESCRIPTION:Title: Fall of Quantum Particle to the Center: Exact solution\nby M.
I. Tribelsky (Faculty of Physics\, M. V. Lomonosov Moscow State University
) as part of Mathematical models and integration methods\n\n\nAbstract\nA
fall of a particle to the center of a singular potential is one of a few f
undamental problems of quantum mechanics. Nonetheless\, its solution is no
t complete yet. The known results just indicate that if the singularity of
the potential is strong enough\, the spectrum of the Schrodinger equation
is not bounded from below. However\, the wave functions of the problem do
not admit the limiting transition to the ground state. Therefore\, the un
boundedness of the spectrum is only a necessary condition. To prove that a
quantum particle indeed can fall to the center\, a wave function describi
ng the fall should be obtained explicitly. This is done in the present pap
er. Specifically\, an exact solution of the time-dependent Schrodinger equ
ation corresponding to the fall is obtained and analyzed. A law for the co
llapse of the region of the wave function localization to a single point i
s obtained explicitly. It is shown that the known necessary conditions for
the particle to fall simultaneously are sufficient.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. V. Schmidt
DTSTART:20211125T110000Z
DTEND:20211125T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/30
DESCRIPTION:Title: Modeling of the far region of a swirling turbulent wake using the
Rodi model\nby A. V. Schmidt as part of Mathematical models and integr
ation methods\n\n\nAbstract\nThe work is devoted to the construction of a
self-similar solution for the far region of a swirling turbulent wake. The
algebraic Rodi model is considered\, which is a simplification of differe
ntial equations for the transfer of components of the Reynolds stress tens
or. A group-theoretic analysis of the model is carried out. The reduced sy
stem was solved numerically using a modified shooting method. A detailed c
omparison of the constructed self-similar solution with results obtained b
y G.G. Chernykh and A.G. Demenkov by direct numerical integration of the m
odel equations is performed.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов
DTSTART:20211209T110000Z
DTEND:20211209T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/31
DESCRIPTION:Title: Интегрируемое уравнение Абеля втор
ого рода\, возникающее при описании асим
птотик симметрийного решения уравнения
Кортевега-де Вриза\nby Б.И. Сулейманов as
part of Mathematical models and integration methods\n\nAbstract: TBA\n\nП
редставлено общее решение обыкновенног
о дифференциального уравнения первого п
орядка с рациональной правой частью\, во
зникающего при построении асимптотик пр
и больших значениях времени совместных
решений уравнения Кортевега-де Вриза и с
тационарной части его высшей неавтономн
ой симметрии\, определяемой линейной ко
мбинацией первой высшей автономной симм
етрии уравнения Кортевега-де Вриза и его
классической симметрии Галилея. По тео
реме о неявной функции данное общее реше
ние локально находится из первого интег
рала\, явно выписанного в терминах гипер
геометрических функций. Частный случай
этого общего решения определяет автомод
ельные решения уравнений Уизема\, найден
ные ранее Г.В. Потеминым в 1988 г. (В известн
ых работах А.В. Гуревича и Л.П. Питаевског
о начала 70-х годов было установлено\, что
данные решения уравнений Уизема в главн
ом порядке описывают возникновение неза
тухающих осциллирующих волн в широком р
яде задач с малой дисперсией.) Результат
статьи вновь подтверждает эмпирическое
правило: из интегрируемых уравнений в ре
зультате различных предельных переходо
в могут получаться лишь в том или ином см
ысле интегрируемые уравнения. Выдвигает
ся общая гипотеза: интегрируемые обыкно
венные дифференциальные уравнения\, под
обные рассматриваемому в статье\, должны
возникать и при описании асимптотик при
больших временах других симметрийных р
ешений эволюционных уравнений\, допуска
ющих применение метода обратной задачи.\
n
LOCATION:https://stable.researchseminars.org/talk/mmandim/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Meleshko (School of Mathematics\, Institute of Science\, Sur
anaree University of Technology\, Nakhon Ratchasima\, Thailand)
DTSTART:20211223T110000Z
DTEND:20211223T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/32
DESCRIPTION:Title: A Method for Finding Reciprocal Transformations\nby S. V. Mele
shko (School of Mathematics\, Institute of Science\, Suranaree University
of Technology\, Nakhon Ratchasima\, Thailand) as part of Mathematical mode
ls and integration methods\n\n\nAbstract\nEquivalence transformations play
one of the important roles in continuum mechanics. These transformations
reduce the original equations to simpler forms. One of the classes of nonl
ocal equivalence transformations is the class of reciprocal transformation
s. Despite the long history of applications of such transformations in con
tinuum mechanics\, there is no method of obtaining them. Recently such a m
ethod was proposed. The method uses group analysis approach and it consist
s of similar steps as for finding equivalence group of transformations. Th
e new method provides a systematic tool for finding classes of reciprocal
transformations (reciprocal equivalence group of transformations). Similar
to the classical group analysis this approach can be also applied for fin
ding all discrete reciprocal transformations (not only composing a group).
For an illustration the method is demonstrated by several models applied
in hydrodynamics. The author is very thankful to Professor Colin Rogers fo
r attracting my attention to reciprocal transformations.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:К.П. Дружков (МГУ)
DTSTART:20220120T110000Z
DTEND:20220120T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/33
DESCRIPTION:Title: О вариационных принципах для уравне
ний пограничного слоя\nby К.П. Дружков (М
ГУ) as part of Mathematical models and integration methods\n\nAbstract:
TBA\n\nВ докладе будут рассмотрены стацион
арные уравнения пограничного слоя в эйл
еровых переменных (при постоянном давле
нии поступательно движущегося внешнего
потока). Для этой системы уравнений буде
т дано полное решение обратной задачи ва
риационного исчисления: будет показано\,
что не существует ни одного функционала
действие\, такого что:\n1) среди его стаци
онарных точек содержатся все решения да
нной системы (и\, быть может\, что-нибудь е
щё)\,\n2) определяемое им соответствие из т
еоремы Нётер нетривиально.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Stepanyants (University of Southern Queensland\, Toowoomba\,
Australia)
DTSTART:20220203T110000Z
DTEND:20220203T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/34
DESCRIPTION:Title: Formation of envelop solitary waves from the localised pulses with
in the Ostrovsky equation\nby Yury Stepanyants (University of Southern
Queensland\, Toowoomba\, Australia) as part of Mathematical models and in
tegration methods\n\n\nAbstract\nWe study the formation of envelope solito
ns from the Korteweg–de Vries (KdV) solitons in the long term evolution
within the framework of the Ostrovsky equation. This equation was derived
by L.A. Ostrovsky in 1978 for the description of weakly nonlinear oceanic
waves affected by the Earth' rotation. Subsequently\, it became clear that
this equation is rather universal\; currently\, it is widely used for the
description of nonlinear waves in various media. This equation is\, appar
ently\, non-integrable and even does not possess steady solitary wave solu
tions in application to media with negative small-scale dispersion. As has
been shown by Grimshaw and Helfrich (2008)\, long-term evolution of initi
al pulses in the form of small-amplitude KdV soliton results in the emerge
nce of envelope solitons which can be described by the nonlinear Schroding
er (NLS) equation. However\, the generalised NLS equation derived by Grims
haw and Helfrich (2008) provides the results which are in contradiction wi
th the numerical simulations. The problem was later revisited by Grimshaw
and Stepanyants (2020) and was shown that the wave packet asymptotically a
ppearing after a long-term evolution of a KdV soliton can be described by
the conventional NLS equation. The solution obtained for an envelope solit
on agrees well with the results of numerical simulations.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:С.М. Чурилов (Институт солнечно-земн
ой физики СО РАН\, Иркутск)
DTSTART:20220217T110000Z
DTEND:20220217T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/35
DESCRIPTION:Title: Безотражательное распространение п
оверхностных волн на мелкой воде в канал
е переменной ширины и глубины на фоне не
однородного течения\nby С.М. Чурилов (Ин
ститут солнечно-земной физики СО РАН\, Ир
кутск) as part of Mathematical models and integration methods\n\n\nAb
stract\nВ приближении мелкой воды рассмотре
на линейная задача о распространении по
верхностных волн на фоне неоднородного
течения идеальной жидкости в канале с из
меняющимися вдоль потока шириной $W(x)$ и г
лубиной $H(x)$ [1\,2]. Найдены три вида соотно
шений\, связывающих скорость течения $U(x)$
и скорость распространения волн $c(x) = \\sqr
t{gH(x)}$\, таких\, что при выполнении любого
из них волны произвольной формы распрос
траняются без отражения как по течению\,
так и против него. В соответствии с этим
выделены три класса безотражательных те
чений и исследованы их свойства. В течен
иях класса А скорости течения и волн свя
заны простым соотношением $c(x)U(x) = \\Pi = \\math
rm{const}$\, обеспечивающим распространение
волн без отражения на любые расстояния\,
т.е. вдоль всей оси $x$. В течениях классов
В и С скорости связаны дифференциальным
уравнением первого порядка (своим в кажд
ом классе)\, которое имеет особые точки. П
оэтому здесь в общем случае регулярные р
ешения существуют лишь на ограниченных
интервалах изменения $x$ (луче или конечн
ом интервале). Для каждого класса найден
ы условия\, при которых есть регулярные р
ешения на всей оси $x$. Кроме того\, показа
но\, что можно конструировать и «составн
ые» безотражательные течения класса В. О
бщий анализ проблемы проиллюстрирован р
ешениями для конкретных соотношений меж
ду глубиной и скоростью течения.\n\nПубли
кации\n\n1. Churilov S.M.\, Stepanyants Yu.A. Reflectionless wave pro
pagation on shallow water with variable bathymetry and current. J. Fluid M
ech. 931\, A 15\, 2022\; arXiv:2108.12549v2 [physics.flu-dyn]\, 2021.\n\n2
. Churilov S.M.\, Stepanyants Yu.A. Reflectionless wave propagation on sha
llow water with variable bathymetry and current. II. arXiv: 2201.00307v1 [
physics.flu-dyn]\, 2022.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ю. В. Брежнев
DTSTART:20220303T110000Z
DTEND:20220303T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/36
DESCRIPTION:Title: Квантовая «ревизия» теоремы Пифаго
ра\nby Ю. В. Брежнев as part of Mathematical models and int
egration methods\n\n\nAbstract\nСтранность этого утвер
ждения только кажущаяся и оно может быть
сформулировано даже более экстравагант
но. Мы даем «единственно правильное» пон
имание\, которое стоит за реальным смысл
ом теоремы Пифагора. Хотя речь идет о кла
ссическом математическом утверждении\,
его переформулировка мотивирована кван
товой темой. А именно\, проблемой пониман
ия и вывода знаменитого правила квантов
ой вероятности - правила Борна\, - которое
записывается через квадрат модуля $|a|^2$.
Если кратко\, то «почему квадрат»? Есть п
рямой ответ на этот вопрос\, а появление
этих квадратов\, модулей и двоек - компле
ксной и обычной вещественной - оказывают
ся совершенно однотипным.\n\nКлючевыми сл
овами к материалу является задача после
довательного логического построения ис
числения (calculus) на векторном пространств
е. Тогда рассмотрение известных правил п
араллелограмма\, неравенства треугольни
ка\, понятия углов\, аксиом скалярного пр
оизведения\, нормы\, топологий и т.д. дост
аточно заменить на задачу построения ко
личественных величин на векторах. Отсюд
а будет следовать сначала собственно Пи
фагорово утверждение и только потом (!) -
вышеуказанные объекты. Теорема\, при это
м\, перестает быть теоремой\, превращаясь
\, грубо говоря\, в некоторое естественно
е минималистическое определение\; подро
бности последуют. Сам квадрат в «теореме
» появляется как единственно возможное
следствие. Перечисленные выше элементы
школьной геометрии становятся\, в свою о
чередь\, производными от Пифагорова квад
рата\, с последующей ревизией первичност
и понятия длины. С квантовыми (комплексн
ыми) аналогами - ситуация точно такая же.
Более того\, именно количественно-статис
тическая идеология и природа квантового
правила Борна дает подсказку к «новому
взгляду на» и наиболее убедительные «об
ъяснения к» этой древней греческой теор
еме.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.V. Kaptsov
DTSTART:20220317T110000Z
DTEND:20220317T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/37
DESCRIPTION:Title: Solutions of the Euler equations and stationary structures in an i
nviscid fluid\nby O.V. Kaptsov as part of Mathematical models and inte
gration methods\n\n\nAbstract\nThe Euler equations describing two-dimensio
nal steady flows of an inviscid fluid are studied. These equations are red
uced to one equation for the stream function and then\, using the Hirota f
unction\, solutions of three nonlinear elliptic equations are found. The s
olutions found are interpreted as sources in a rotating fluid\, jets\, cha
ins of sources and sinks\, vortex structures. We propose a new simple meth
od for constructing solutions in the form of rational expressions of ellip
tic functions. It is shown that the flux of fluid across a closed curve is
quantized in the case of the elliptic Sin-Gordon equation.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.P. Tsarev (Siberian Federal University\, Krasnoyarsk)
DTSTART:20220331T110000Z
DTEND:20220331T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/38
DESCRIPTION:Title: Generalized factorization of second-order linear partial different
ial operators and reflectionless wave propagation in shallow water\nby
S.P. Tsarev (Siberian Federal University\, Krasnoyarsk) as part of Mathem
atical models and integration methods\n\n\nAbstract\nThis talk will be dev
oted to an interpretation of a recent talk by S.M. Churilov and Yu.A. Step
anyants (Reflectionless propagation of surface waves in shallow water in a
channel of variable width and depth against the background of an inhomoge
neous flow\, https://researchseminars.org/talk/mmandim/35/) from the point
of view of the theory of generalized factorization of differential operat
ors ([1]).\n\nAs shown in the works of S.M. Churilov\, Yu.A. Stepanyants e
t al. ([2])\, the factorization of a second-order operator with two indepe
ndent variables\, which describes the propagation of waves in an inhomogen
eous one-dimensional medium\, into a product of first-order operators resu
lts in the appearance of a large family of solutions that describe\, from
a physical point of view\, waves that can be considered propagating withou
t reflection from inhomogeneities.\n\nWe will expose briefly the theory of
generalized factorization of second-order partial differential operators\
, originating from the works of outstanding mathematicians of the 19th - e
arly 20th century P.-S. Laplace\, G. Darboux\, E. Goursat and others and f
urther developed at the end of the 20th century.\n\nThe generalized factor
ization theory allows us to substantially expand the class of reflectionle
ss solutions.\n\nReferences:\n\n[1] E.I. Ganzha\, S.P. Tsarev\, "Classical
methods of integration of hyperbolic systems and equations of the second
order"\, 2007\, KSPU (in Russian)\, http://dx.doi.org/10.13140/2.1.4535.80
84 The full text is available at the link: https://www.researchgate.net/pr
ofile/Sergey-Tsarev/publication/235993531_Klassiceskie_metody_integrirovan
ia_giperboliceskih_sistem_i_uravnenij_vtorogo_poradka/links/0c96051550c728
03c2000000/Klassiceskie-metody-integrirovania-giperboliceskih-sistem-i-ura
vnenij-vtorogo-poradka.pdf\n\n[2] Churilov\, Semyon M.\, and Yury A. Stepa
nyants. "Reflectionless wave propagation on shallow water with variable ba
thymetry and current." Journal of Fluid Mechanics 931 (2022).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.B. Borisov
DTSTART:20220414T110000Z
DTEND:20220414T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/39
DESCRIPTION:Title: O(3)-model: Integrability. Stationary and Dynamic Magnetic Structu
res\nby А.B. Borisov as part of Mathematical models and integration m
ethods\n\n\nAbstract\nA three-dimensional O(3)-model for a unit vector $n(
r)$ has numerous application\nin the field theory and in the physics of co
ndensed matter. We prove that this model\nis integrable under some differe
ntial constraint\, that is\, under certain restrictions for the\ngradients
of fields $Θ(r)$\, $Φ(r)$\, parametrizing the vector $n(r)$). Under th
e presence of the\ndifferential constraint\, the equations of the models a
re reduced to a one-dimensional sine-\nGordon equation determining the dep
endence of the field $Θ(r)$ on an auxiliary field $a(r)$\nand to a system
of two equations $(∇S)(∇S) = 0$\, $\\Delta S = 0$ for a complex-value
d function\n$S(r) = a(r)+i\\cdot Φ(r)$. We show that the solution of this
system provide all known before exact\nsolutions of models\, namely\, two
-dimensional magnetic instantons and three-dimensional\nstructures of hedg
ehog type.\n\nWe show that the found in this way exact solution of the sys
tem for the field $S(r)$ leads one to exact solution of equations of O(3)
–model in the form of an arbitrary implicit function of two variables. T
wo simple solutions of these equations are discussed: a new magnetic struc
ture that represents two straight intersecting vortex threads and a "inclu
sion" type structure.\n\nThe integrability of the dynamical equations the
O(3)-model in four-dimensional pseudo-Euclidean space–time was investiga
ted . We use a differential substitution to reduce the equations to the on
e-dimensional sine-Gordon equation and a system of two equations for a com
plex-valued function $S(r\, t)$ that uniquely determines a vector $n$. We
prove that solving the equations for this function amounts to solving a sy
stem of four quasilinear equations for auxiliary fields. We obtain their e
xact solution in the form of an implicit function of three variables\, whi
ch then determines the exact solutions of the dynamical equations with dif
ferential constraints taken into account. As examples\, we describe the dy
namics of a plane vortex in D = (2.1)\, a “hedgehog”-type structure\,
and new dynamical topological structure.\n\nReferences:\n\n1. А.Б. Бо
рисов. Трехмерные вихри в модели Гейзенб
ерга\, ТМФ\, 2021\, том 208\, номер 3\, 471–480 (A.B. Bor
isov. Three-Dimensional Vortices in the Heisenberg Model. Theoretical and
Mathematical Physics\, 208(3): 1256–1264 (2021)).\n\n2. А.Б. Бори
сов. Об интегрируемости 𝑂(3)–модели. Уфи
мский математический журнал. Том 13. № 2 (20
21). С. 6-10 (А.B. Borisov\, On integrability of O(3)–model\, Ufimsk.
Mat. Zh.\, 2021\, Volume 13\, Issue 2\, 6–10).\n\n3. А.Б. Борисо
в. Динамика трехмерных магнитных структ
ур в модели Гейзенберга. ТМФ\, 2022\, том 210\,
номер 1\, страницы 115–127 (A.B. Borisov. Dynamics of Three
-Dimensional Magnetic Structures in the Heisenberg Model. Theoretical and
Mathematical Physics\, 210(1): 99–110 (2022)).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Захар Макридин (ИГиЛ\, Новосибирск)
DTSTART:20220428T110000Z
DTEND:20220428T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/40
DESCRIPTION:Title: Ветвление периодических решений и з
аконы сохранения нелинейных уравнений т
еории волн (по материалам кандидатской д
иссертации)\nby Захар Макридин (ИГиЛ\, Но
восибирск) as part of Mathematical models and integration methods
\n\n\nAbstract\nВ настоящей диссертации рассма
триваются два типа задач математической
теории нелинейных волн. Первый тип связ
ан с построением семейств асимптотическ
их периодических решений системы слабос
вязанных обыкновенных дифференциальных
уравнений\, которая получается при пере
ходе к бегущей переменной в модельной си
стеме зацепленных уравнений Кортевега
— де Фриза. В задачах второго типа иссле
дуются способы построения трехмерных за
конов сохранения коммутирующих интегри
руемых гидродинамических цепочек и их р
едукций.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Depar
tment of Physical Oceanography\, Woods Hole Oceanographic Institution\, Wo
ods Hole\, MA USA. ** Department of Applied Mathematics\, University of Co
lorado\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Compu
ting\, University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Austra
lia)
DTSTART:20220512T120000Z
DTEND:20220512T130000Z
DTSTAMP:20260404T111326Z
UID:mmandim/41
DESCRIPTION:Title: Joint Effects of Rotation and Topography on Internal Solitary Wave
s\nby K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Dep
artment of Physical Oceanography\, Woods Hole Oceanographic Institution\,
Woods Hole\, MA USA. ** Department of Applied Mathematics\, University of
Colorado\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Com
puting\, University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Aust
ralia) as part of Mathematical models and integration methods\n\n\nAbstrac
t\nWe present the results of the recent study of dynamics of nonlinear oce
anic solitary waves under the influence of the combined effects of nonline
arity\, Earth’s rotation\, and depth inhomogeneity. Our consideration is
based on the extended model of the Korteweg–de Vries (KdV) equation tha
t in general accounts for the quadratic and cubic nonlinearity (the Gardne
r equation) with the additional terms incorporating the effects of rotatio
n and slowly varying depth. After a brief historical outline\, using the a
symptotic (adiabatic) theory\, we describe a complex interplay between the
se factors. As an application\, the case of a two-layer fluid with the var
iable-depth lower layer is considered using the approximate theory\, as we
ll as through numerical solutions of the governing equation that includes
all the above factors under realistic oceanic conditions. In particular\,
different scenarios of the soliton propagating toward the “internal beac
h” (e.g.\, zero lower-layer depth) are studied in which the terminal dam
ping can be caused by radiation or disappearing quadratic nonlinearity (wh
en the layers’ depths become equal). We also consider interaction of a s
oliton with a long wave providing the energy “pump” compensating the r
adiation losses due to rotation so that the soliton can exist infinitely.
The limitations of the adiabatic approach due to the radiation and other f
actors are also demonstrated.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Слюняев (Институт прикладной фи
зики РАН\, Нижний Новгород)
DTSTART:20220526T110000Z
DTEND:20220526T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/42
DESCRIPTION:Title: Морские волны-убийцы: проблема\, зад
ачи и решения\nby А.В. Слюняев (Институт
прикладной физики РАН\, Нижний Новгород)
as part of Mathematical models and integration methods\n\n\nAbstract\nПр
едлагается обзор исследований\, связанн
ых с т.н. морскими волнами-убийцами — нео
жиданно высокими волнами\, по некоторым
данным появляющимися слишком часто\, чем
ожидается. Формулируется проблема океа
нологии в ее сегодняшнем понимании\, обо
значаются направления исследований и по
ставленные перед ними задачи\, обсуждают
ся уже полученные результаты.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosib
irsk\, Russia)
DTSTART:20220929T110000Z
DTEND:20220929T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/43
DESCRIPTION:Title: Nonlinear stationary internal waves in a weakly stratified fluid\nby Nikolay Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosibi
rsk\, Russia) as part of Mathematical models and integration methods\n\n\n
Abstract\nWe consider three classes of problems related to the constructio
n and analysis of asymptotic solutions of the Euler equations for an invis
cid inhomogeneous fluid.\n\n1. Stationary solutions such as solitary- and
periodic waves in a continuously stratified fluid\, and their limiting reg
imes\n\n2. Parametric families of solutions of the 2.5-layer model of nonl
inear long waves and their applications in oceanology\n\n3. Stationary wav
e structures and trapped solitary waves over an uneven bottom\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM\, Krasnoyarsk\, Russia)
DTSTART:20221013T110000Z
DTEND:20221013T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/44
DESCRIPTION:Title: Some solutions of the Euler system of an inviscid incompressible f
luid\nby Oleg Kaptsov (ICM\, Krasnoyarsk\, Russia) as part of Mathemat
ical models and integration methods\n\n\nAbstract\nWe consider a system of
two-dimensional Euler equations describing the motions of an inviscid inc
ompressible fluid. It reduces to one non-linear equation with partial deri
vatives of the third order. A group of point transformations allowed by th
is equation is found. Some invariant solutions and solutions not related t
o invariance are constructed. The solutions found describe vortices\, jet
streams\, and vortex-like formations.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.B. Borisov\, D.V. Dolgikh
DTSTART:20221027T110000Z
DTEND:20221027T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/45
DESCRIPTION:Title: Integration of the equations of the Heisenberg model (2D) and the
chiral SU(2) models by differential geometry methods\nby A.B. Borisov\
, D.V. Dolgikh as part of Mathematical models and integration methods\n\n\
nAbstract\nIn the report\, to integrate the two-dimensional Heisenberg equ
ation and the three-dimensional chiral SU(2) model\, the differential-geom
etric method of integration is used\, the essence of which is as follows.
First\, we perform the hodograph transformation\, i.e. change the role of
dependent and independent coordinates. Unlike the standard hodograph trans
formation\, we do not just introduce derivatives of the old coordinates wi
th respect to new ones\, but define through these derivatives new fields a
ssociated with the components of the metric tensor that appears when the h
odograph transformation is performed. Since the original independent coord
inates were Euclidean\, the curvature tensor in terms of the introduced me
tric must vanish. Ultimately\, we obtain a self-consistent system of equat
ions for calculating the components of the metric tensor. In this case\, t
he equations guaranteeing the curvature tensor to vanish turn out to be th
e main ones\, and the system of nonlinear equations of the models is their
reduction. The solutions of the constructed equations make it possible to
write the solutions of the original models in the form of implicit functi
ons. It is important that the differential-geometric method of model integ
ration\, based on the embedding of a non-linear partial differential equat
ion in a certain differential relation in Euclidean space\, makes it possi
ble to analyze a wide variety of spatial structures\, the study of which b
y other methods is extremely difficult. The solutions found in the chiral
SU(2) model describe three-dimensional configurations containing\, in part
icular\, spatial vortices\, sources\, non-localized textures\, and structu
res with a mapping degree equal to one\, similar to topological solitons.
In the Heisenberg model we find a vortex strip (a limited vortex region in
a plane). Many of the obtained solutions depend on arbitrary functions.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay A. Kudryashov (MEPhI\, Moscow)
DTSTART:20221110T110000Z
DTEND:20221110T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/46
DESCRIPTION:Title: From the Painlevet test to methods for constructing analytical sol
utions of nonlinear ODEs\nby Nikolay A. Kudryashov (MEPhI\, Moscow) a
s part of Mathematical models and integration methods\n\n\nAbstract\nThe a
pplication of the Painlevet test to analyze nonlinear ordinary differentia
l equations is discussed. A brief review of classical works by S. V. Koval
evskaya on solving the problem of motion of a rigid body with a fixed poin
t and works by P. Penleve on the classification of one class of second-ord
er equations is given. The well-known example of the Korteweg–de Vries e
quation taking into account the traveling wave solutions illustrates the P
ainlevet property for a nonlinear oscillator. Special attention is paid to
non-integrable partial differential equations such as the Korteweg–de V
ries–Burgers equation and the Kuramoto–Sivashinsky equation. Using tra
veling wave solutions\, the construction of analytical solutions to these
equations is illustrated. Possible applications of the simplest equations
method for constructing analytical solutions of non-integrable differentia
l equations are discussed. The application of the method for constructing
optical solitons of a generalized nonlinear Schrodinger equation of unrest
ricted order with nonlinearity in the form of a polynomial is illustrated
.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics\, Irkutsk)
DTSTART:20221124T110000Z
DTEND:20221124T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/47
DESCRIPTION:Title: On the stability of sharply stratified shear flows with inflection
-free velocity profiles\nby S.M. Churilov (Institute of Solar-Terrestr
ial Physics\, Irkutsk) as part of Mathematical models and integration meth
ods\n\n\nAbstract\nWe study the linear stability of shear flows with sharp
stratification ($l \\ll L$\, where $l$ and $L = 1$ are vertical scales of
density and velocity variation respectively) and a monotonic velocity pro
file $V_x = U(z)$ which has no inflection points and increases from $U = 0
$ at the bottom ($z = 0$) to $U = 1$ when $z \\to +\\infty$\, $U'(0) = 1$.
We show that such a flow with step density variation ($l = 0$) and $U'' <
0$ has the instability domain of an universal form on the ($k$\, $J$) pla
ne\, where $k$ is the wave number and $J$ is the bulk Richardson number. N
amely\, the\ndomain is bounded by abscissa axis ($J = 0$)\, dispersion cur
ve $J = J(k\, c = 1)\,$ and\nthe segment of ordinate axis ($k = 0$) connec
ting them. Here $c$ is the phase velocity\nof the wave. The role of null-c
urvature points on the velocity profile (where\n$U'' = 0$\, but does not c
hange its sign) in the transformation of such an instability\ndomain into
that of a flow with a piecewise linear velocity profile is discussed.\n\nI
t is shown that in continuously stratified flows with $0 < l \\ll 1$\, a c
ountable\ninfinity of oscillation modes appears with $J = J_m(k\,c)$\, $m
= 0\,1\,2\,\\ldots$. For any $m$\,\nstreamwise propagating (i.e.\, $y$-ind
ependent) waves have instability domain\nextending from the upper boundary
\,\n\n$J = J_0^{(+)}(k) = J_0(k\,c=1) = O(1)$ or $J = J_m^{(+)}(k) = J_m(k
\,c=1) = O(m^2l^{-1})$\, $m \\ge 1$\nto the lower one\,\n\n$J = J_0^{(-)}(
k) > 0$\, where $J_0^{(-)}(k) = O(l^2)$ when $l < k < 1$\, or\n\n$J = J_m^
{(-)}(k) > 0$\, where $J_m^{(-)}(k) = O(m^2l)$ when $l^{3/2} < k < l^{1/2}
$\, $m \\ge 1$.\n\nBy virtue of Squire's theorem\, the lower "stability ba
nds" (between $J_m^{(-)}(k)$ and the\n$J = 0$ axis) are filled with unstab
le oblique waves. When $J$ is in the range from\n$O(l^2)$ to $O(l)$\, unst
able oblique and streamwise propagating waves (mainly\nbelonging to $m = 0
$ mode) successfully compete\, and a wide spectrum of three-\ndimensional
unstable waves with close streamwise phase velocities and\ncomparable grow
th rates is excited.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. D. Yunakovsky
DTSTART:20221208T110000Z
DTEND:20221208T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/48
DESCRIPTION:Title: Methods for numerical simulation of NLS\nby A. D. Yunakovsky a
s part of Mathematical models and integration methods\n\n\nAbstract\nThe a
dvent of supercomputers made it possible to model multidimensional NLS and
revealed new problems: new parallelizable algorithms were required.\n\nFo
r equations of the "parabolic" type\, which include the non-stationary Sch
rödinger equation\, numerical schemes have very stringent stability condi
tions: $\\Delta t < \\Delta x^2$\, which\, in fact\, slows down the soluti
on of the problem when the grid is refined. In addition\, in equations of
the NLSE type\, high spatial harmonics do not decay with time\, but have r
apidly changing phases\, which leads even under a "relatively mild" condit
ion of stability to the phenomenon of random phases.\n\nA review of grid a
nd spectral methods for finding approximate solutions of the NSE is given\
, and the possibilities of using the FFT are analyzed. The problem of incr
easing the counting step with respect to time and typical errors are discu
ssed. Brief reviews of the use of the operator exponential method and the
method of nonreflecting boundary conditions are given. The possibilities o
f the hyperbolization method for NLS are discussed.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. P. Tsarev (Siberian Federal University\, Krasnoyarsk)
DTSTART:20221222T110000Z
DTEND:20221222T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/49
DESCRIPTION:Title: The Monge problem: From quadrature-free integration of underdeterm
ined nonlinear ODEs to efficient car parking\nby S. P. Tsarev (Siberia
n Federal University\, Krasnoyarsk) as part of Mathematical models and int
egration methods\n\n\nAbstract\nThis talk is about an old topic of finding
closed-form solutions of UNDERDETERMINED systems of nonlinear ordinary di
fferential equations\, started by G.Monge in 1784 and later followed by Go
ursat (1905)\, Hilbert (1913) and Cartan (1914).\n\nIn the last decades of
the XX century these problems draw attention of specialists in nonlinear
control. In particular\, the technique of this problem was used in develop
ing motion algorithms for nonholonomic mechanical systems\, a typical exam
ple being a car with N trailers. Parking such a "car train" moving back is
a popular difficult task! Modern results based on the old investigations
of Goursat make automatic control of such vehicles possible.\n\nFor those
interested in the problem of integration of ODEs and PDEs: using the resul
ts described one can often remove (unnecessary) quadratures in the final e
xpressions for the complete solution of a C-integrable nonlinear PDEs.\n\n
We expose the classical results by Cartan and Hilbert showing the intruigi
ng details of the Monge problem.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M.Churilov\, I.G. Shukhman (Institute of Solar-Terrestrial Physi
cs\, Irkutsk)
DTSTART:20230126T110000Z
DTEND:20230126T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/50
DESCRIPTION:Title: Critical layer and weakly nonlinear evolution of unstable quasi-mo
nochromatic perturbations in shear flows\nby S.M.Churilov\, I.G. Shukh
man (Institute of Solar-Terrestrial Physics\, Irkutsk) as part of Mathemat
ical models and integration methods\n\n\nAbstract\nBy Howard’s semicircl
e theorem\, in a plane-parallel shear flow\, the real part of the phase ve
locity $c$ of an unstable perturbation $\\sim f(z)\\exp[ik(x-ct)]$ is betw
een the minimum and maximum of the flow velocity $V_x = U(z)$ and coincide
s with $U$ on a critical level $z=z_c$ so that $\\mathrm{Re} \\\, c = U(z_
c)$. In a narrow neighborhood of this level\, — so called critical layer
(CL)\, — liquid particles are in phase resonance with the wave and inte
nsively interact with it. In the framework of an idealized statement of th
e problem taking no account of dissipation (viscosity)\, unsteadiness\, an
d nonlinearity\, the perturbation eigenfunction $f(z)$ is singular on the
critical level. Taking into consideration any one of these factors makes t
he solution regular\, but the relative magnitude of the perturbation insid
e the CL remains large. For this reason\, it is the CL that makes the lead
ing-order contribution into nonlinear interactions\, and this fact simplif
ies the study of a weakly nonlinear evolution of an unstable perturbation.
\n\nEach of these factors specifies the length scale associated with it\,
namely\,\n\n(i) viscous $L_ν = (k^3 \\mathrm{Re})^{-1/3} = O(ν^{1/3})$\,
\n\n(ii) unsteady $L_t = |(kU'_c A)^{-1} d|A|/dt| = O(γ)$\,\n\n(iii) nonl
inear $L_N \\sim |A/U'_c|^δ$\,\n\nwhere $\\mathrm{Re}$ is Reynolds number
\, $A(t)$ is the perturbation amplitude\, $δ$ depends on the behavior of
$f(z)$ in the neighborhood of the critical level\, and the prime denotes t
he derivative in $z$. The greatest of these scales determines not only the
width of the CL\, but also the behavior of the solution inside it. Theref
ore\, it is appropriate to distinguish between viscous\, unsteady\, and no
nlinear CLs\, taking into account that the CL kind may change in the proce
ss of evolution in accordance with the scale ratio.\n\nAs a result\, only
a limited number of basic scenarios of evolution do exist. The realization
of one scenario or another\, or some sequence of them depends mainly on t
he degree of supercriticality of the basic unstable flow and on the nature
of the singularity at the critical level.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. В. Боровских (МГУ)
DTSTART:20230209T110000Z
DTEND:20230209T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/51
DESCRIPTION:Title: Групповой анализ уравнения эйконал
а\nby А. В. Боровских (МГУ) as part of Mathematical mod
els and integration methods\n\n\nAbstract\nВ докладе будут п
редставлены результаты группового анал
иза уравнения эйконала — уравнения\, опи
сывающего фронт распространяющейся вол
ны. Актуальность такого анализа возникл
а в связи с исследованием распространен
ия волн в неоднородной и анизотропной ср
еде. В волновой теории обычно предполага
ется\, что эйконал уже известен\, а на сам
ом деле для каких сред (кроме каноническ
ой однородной) уравнение эйконала можно
проинтегрировать — было неизвестно.\n\nГ
рупповая классификация сначала трехмер
ных\, затем двумерных\, а в конце концов —
анизотропных уравнений показала\, что з
адача групповой классификации оказывае
тся наиболее содержательной и продуктив
ной только в наиболее общей постановке.
Именно тогда обнаруживаются четкие связ
и с геометрией\, физикой и аналитическим
и свойствами уравнений. Именно поэтому п
олученная классификация\, вместе со всей
совокупностью указанных связей\, может
рассматриваться как образцовая.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M.Churilov (Institute of Solar-Terrestrial Physics\, Irkutsk)
DTSTART:20230302T110000Z
DTEND:20230302T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/52
DESCRIPTION:Title: Weakly-nonlinear stage of instability development in shear flows w
ith an inflection-free velocity profile and thin pycnocline\nby S.M.Ch
urilov (Institute of Solar-Terrestrial Physics\, Irkutsk) as part of Mathe
matical models and integration methods\n\n\nAbstract\nWeakly stratified fl
ows of the class under study have a wide 3D spectrum of unstable waves wit
h very close growth rates. What is more\, their phase velocities differ li
ttle and therefore their individual critical layers merge into a common on
e. On this basis\, nonlinear evolution equations describing the perturbati
on development are derived and analyzed. Their solutions demonstrate that\
, throughout a weakly nonlinear stage of development\, wave amplitudes gro
w explosively. During the first (three-wave) phase\, the most rapidly grow
ing are low-frequency waves whereas at the next phase\, when numerous and
diverse higher-order wave interactions come into play\, the growth of high
-frequency waves is accelerated and they overtake low-frequency waves. The
results obtained are illustrated by numerical calculations for some ensem
bles of waves.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E.A. Kuznetsov (P.N. Lebedev Physical Institute of RAS\, Moscow\,
Russia)
DTSTART:20230316T110000Z
DTEND:20230316T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/53
DESCRIPTION:Title: Folding in fluids\nby E.A. Kuznetsov (P.N. Lebedev Physical In
stitute of RAS\, Moscow\, Russia) as part of Mathematical models and integ
ration methods\n\n\nAbstract\nThe formation of the coherent vortical struc
tures in the form of thin pancakes for three-dimensional flows is studied
at the high Reynolds regime when\, in the leading order\, the development
of such structures can be described within the Euler equations for ideal
incompressible fluids. Numerically and analytically on the base of the vor
tex line representation [1\, 2] we show that compression of such structure
s and respectively increase of their amplitudes are possible due to the co
mpressibility of the vorticity in the 3D case [3]. It is demonstrated that
this growth has an exponential behavior and can be considered as folding
(analog of breaking) for the divergence-free fields of vorticity. At high
amplitudes this process in 3D has a self-similar behavior connected the ma
ximal vorticity and the pancake width by the relation of the universal typ
e [4].\n\n[1] E.A. Kuznetsov\, V.P. Ruban\, Hamiltonian dynamics of vortex
lines for systems of the hydrodynamic type\, Pis’ma ZhETF \, 76\, 1015
(1998) [JETP Letters\, 67\, 1076-1081 (1998)].\n\n[2] E.A. Kuznetsov\, Vor
tex line representation for flows of ideal and viscous fluids \, Pis’ma
v ZHETF\, 76\, 406-410 (2002) [JETP Letters\, 76\, 346-350 (2002)].\n\n[3]
D.S. Agafontsev\, E.A. Kuznetsov\, A.A. Mailybaev\, and E.V. Sereshchenko
\, Compressible vortex structures and their role in the hydrodynamical tur
bulence onset\, UFN 192\, 205-225 (2022) [Physics Uspekhi\, 65 189 - 208 (
2022)].\n\n[4] D.S. Agafontsev\, E.A. Kuznetsov and A.A. Mailybaev\, Devel
opment of high vorticity structures and geometrical properties of the vort
ex line representation\, Phys. Fluids 30\, 095104-13 (2018)\; Stability of
tangential discontinuity for the vortex pancakes\, Pisma ZHETF\, 114\, 67
-71 (2021) [JETP Letters\, 2021\, 114\, 71–75 (2021)].\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Y. Stepanyants (University of Southern Queensland)
DTSTART:20230330T110000Z
DTEND:20230330T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/54
DESCRIPTION:Title: Solitary waves in the cylindrical Kadomtsev–Petviashvili equatio
n\nby Y. Stepanyants (University of Southern Queensland) as part of Ma
thematical models and integration methods\n\n\nAbstract\nWe present exact
solutions in the form of solitary waves in the cylindrical Kadomtsev–Pet
viashvili (cKP) equation (alias Johnson equation) which describes nonlinea
r wave processes in dispersive media. This equation belongs to the class o
f completely integrable systems\; however\, its exact solutions were not s
tudied in detail albeit some particular solutions were found. We show that
this equation has relationships with the classical Korteweg–de Vries an
d plane Kadomtsev–Petviashvili equations. Using these relationships\, so
me new solutions can be formally obtained that represent cylindrically div
erging solitary waves and compact solitary waves called lumps. We demonstr
ate interesting properties of lumps solutions specific for the cylindrical
geometry. Exact solutions describing normal and anomalous lump interactio
ns are found and graphically illustrated.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:М.В. Павлов (ФИАН\, Москва)
DTSTART:20230413T110000Z
DTEND:20230413T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/55
DESCRIPTION:Title: Эллиптические ортогональные систем
ы координат и разделение переменных в оп
ераторе Лапласа\nby М.В. Павлов (ФИАН\, Мо
сква) as part of Mathematical models and integration methods\n\n\nAbst
ract\nРазделение переменных в системах ура
внений в частных производных — одна из в
ажных и интересных задач. Прекрасный обз
ор этой области был представлен в книге
Э. Т. Уиттекера и Дж. Н. Ватсона в 1905 году.\n
\nВ докладе будет предложена интерпретац
ия известных результатов\, которая позво
лит лучше понять препятствия и возможно
сти в теории разделения независимых пер
еменных.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K.R. Khusnutdinova (Department of Mathematical Sciences\, Loughbor
ough University\, UK)
DTSTART:20230427T110000Z
DTEND:20230427T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/56
DESCRIPTION:Title: On elliptic cylindrical Kadomtsev-Petviashvili equation for surfac
e waves\nby K.R. Khusnutdinova (Department of Mathematical Sciences\,
Loughborough University\, UK) as part of Mathematical models and integrati
on methods\n\n\nAbstract\nThere exist two classical versions of the Kadomt
sev-Petviashvili (KP) equation [1]\, related to the Cartesian and cylindri
cal geometries of the waves (derivations for surface waves were given in [
2] and [3]\, respectively). We derived and studied a version related to th
e elliptic-cylindrical geometry in [4] (joint work with Klein\, Matveev an
d Smirnov). The derivation was given from the full set of Euler equations
for surface gravity waves with the account of surface tension. The ecKP eq
uation contains a parameter\, and it reduces to the cKP equation both when
this parameter tends to zero\, and when the solutions are considered at d
istances much larger than that parameter. We showed that there exist trans
formations between all three versions of the KP equation associated with t
he physical problem formulation (KP\, cKP and ecKP equations)\, and used t
hem to obtain new classes of approximate solutions for the Euler equations
. The solutions exist on the whole plane (at least formally). We hope tha
t they could be useful in describing an intermediate asymptotics for the p
roblems where sources\, boundaries and obstacles have elliptic or nearly-e
lliptic geometry.\n\nReferences:\n\n[1] B.P. Kadomtsev\, V.I. Petviashvili
\, On the stability of solitary waves in weakly dispersing media\, Sov. Ph
ys. Dokl.\, 15 (1970) 539-541.\n\n[2] M.J. Ablowitz and H. Segur\, On the
evolution of packets of water waves\, J. Fluid Mech.\, 92 (1979) 691-715.\
n\n[3] R.S. Johnson\, Water waves and Korteweg - de Vries equations\, J. F
luid Mech.\, 97 (1980) 701-719.\n\n[4] K.R. Khusnutdinova\, C. Klein\, V.B
. Matveev\, A.O. Smirnov\, On the integrable elliptic cylindrical Kadomtse
v-Petviashvili equation\, Chaos 23 (2013) 013126.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов (Институт математики
с вычислительным центром УФИЦ РАН\, Уфа)
DTSTART:20230511T110000Z
DTEND:20230511T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/57
DESCRIPTION:Title: Мероморфность решений широкого кла
сса обыкновенных дифференциальных урав
нений типа Пенлеве\nby Б.И. Сулейманов (И
нститут математики с вычислительным цен
тром УФИЦ РАН\, Уфа) as part of Mathematical models and inte
gration methods\n\n\nAbstract\nДоклад основан на двух
совместных с А.В. Домриным и М.А. Шумкиным
публикациях.\n\n1. Домрин А. В.\, Сулейманов
Б.И.\, Шумкин М. А. О глобальной мероморфн
ости решений уравнений Пенлеве и их иера
рхий. Анализ и математическая физика\, Сб
орник статей. К 70-летию со дня рождения п
рофессора Армена Глебовича Сергеева\, Тр
. МИАН\, 311\, МИАН\, М.\, 2020\, 106–122 (A. V. Domrin\, \, B.
I. Suleimanov \, and M. A. Shumkin. Global Meromorphy of Solutions of the
Painlevé Equations and Their Hierarchies. Proceedings of the Steklov Ins
titute of Mathematics\, 2020\, Vol. 311\, Issue 1\, pp. 98–113).\n\n2. V
. Domrin\, M. A. Shumkin and B. I. Suleimanov. Meromorphy of solutions for
a wide class of ordinary differential equations of Painlevé type. Journa
l of Mathematical Physics. Vol.: 63. Issue 2 (2022).\n\nОтталкива
ясь от на результатов А.В. Домрина о лока
льной по времени мероморфной продолжимо
сти из области аналитчности решений сол
итонных уравнений параболического типа\
, в докладе будет доказана мероморфност
ь решений начальных задач для широкого к
ласса обыкновенных дифференциальных ур
авнений. Эти обыкновенные дифференциал
ьные уравнения задаются инвариантными м
ногообразиями нелинейных уравнений в ча
стных производных параболического типа\
, интегрируемых методом обратной задачи
рассеяния. В качестве примеров рассмотр
ены случаи некоторых из уравнений Пенле
ве и их иерархий.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. I. Kaptsov (Suranaree University of Technology\, Thailand)
DTSTART:20230525T110000Z
DTEND:20230525T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/58
DESCRIPTION:Title: Methods for constructing invariant conservative finite-difference
schemes for hydrodynamic-type equations\nby E. I. Kaptsov (Suranaree U
niversity of Technology\, Thailand) as part of Mathematical models and int
egration methods\n\n\nAbstract\nWhen choosing suitable finite-difference s
chemes for equations of hydrodynamic type\, preference is given to various
properties of schemes\, such as their monotonicity\, stability\, conserva
tion of phase volumes\, etc. In the present report\, we focus on the crite
rion of invariance of schemes\, i.e. we consider finite-difference equatio
ns and meshes that preserve the symmetries of the original differential eq
uations.\n\nFor equations of the hydrodynamic type\, the construction of i
nvariant difference schemes is often significantly simplified if the equat
ions are considered in Lagrange coordinates. In this case\, uniform orthog
onal meshes can be used\, which retain their geometric structure under the
action of group transformations inherited from the original equations. In
addition\, in Lagrangian coordinates\, it is easier to find conservation
laws both for differential equations and for the corresponding invariant
difference schemes. In a number of cases\, it is possible to construct inv
ariant conservative schemes that possess difference analogues of all local
conservation laws of the original models.\n\nThe report is primarily devo
ted to the practical aspects of designing schemes of the described type. F
or this\, a number of special techniques and methods have been developed.
The most convenient is the finite-difference analogue of the direct method
\, as well as the technique of constructing schemes based on approximation
s of conservation laws.\nVarious equations of the theory of shallow water
and one-dimensional equations of magnetohydrodynamics are considered as ex
amples.\n\nReferences\n\n1. Dorodnitsyn V. A.\, Kaptsov E. I.\, Discrete s
hallow water equations preserving symmetries and conservation laws. J. Mat
h. Phys.\, 62(8):083508\, 2021.\n\n2. Kaptsov E. I.\, Dorodnitsyn V. A.\,
Meleshko S. V.\, Conservative invariant finite-difference schemes for the
modified shallow water equations in Lagrangian coordinates. Stud. Appl. Ma
th.\, 2022\; 149: 729–761.\n\n3. Dorodnitsyn V. A.\, Kaptsov E. I.\, and
Meleshko S. V.\, Symmetries\, conservation laws\, invariant solutions and
difference schemes of the one-dimensional Green–Naghdi equations. J. No
nlinear Math. Phys.\, 28:90–107\, 2020.\n\n4. Cheviakov A. F.\, Dorodnit
syn V. A.\, Kaptsov E. I.\, Invariant conservation law-preserving discreti
zations of linear and nonlinear wave equations\, J. Math. Phys.\, 61 (2020
) P. 081504.\n\n5. Dorodnitsyn V. A.\, Kaptsov E. I.\, Invariant finite-di
fference schemes for plane one-dimensional MHD flows that preserve conserv
ation laws. Mathematics\, 10(8):1250\, 2022.\n\n6. Kaptsov E. I.\, Dorodni
tsyn V. A.\, Invariant conservative finite-difference schemes for the one-
dimensional shallow water magnetohydrodynamics equations in Lagrangian coo
rdinates. Submitted. Preprint: ht
tps://arxiv.org/abs/2304.03488.\n\n7. Kaptsov E. I.\, Dorodnitsyn V. A
.\, Meleshko S. V.\, Invariant finite-difference schemes for cylindrical o
ne-dimensional MHD flows with conservation laws preservation. Submitted. P
reprint: http://dx.doi
.org/10.48550/arXiv.2302.05280.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:К. Дружков (Российско-Армянский унив
ерситет\, Ереван)
DTSTART:20230921T110000Z
DTEND:20230921T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/59
DESCRIPTION:Title: Внутренние лагранжианы как вариаци
онные принципы\nby К. Дружков (Российско
-Армянский университет\, Ереван) as part of Math
ematical models and integration methods\n\n\nAbstract\nКлассичес
кий принцип стационарного действия связ
ан с лагранжианами\, определёнными на пр
остранствах джетов. Соответствующие ура
внения движения представляют собой пове
рхности в таких пространствах. Оказывае
тся\, что в дополнение к этому принцип ст
ационарного действия всегда воспроизво
дит себя на уровне внутренней геометрии
соответствующего вариационного уравнен
ия. При этом возникает «внутренний интег
ральный функционал»\, определённый на кл
ассе особых подмногообразий уравнения.
Эти подмногообразия имеют размерность к
ак у решений и склеены из начально-краев
ых условий\, продолженных на старшие про
изводные\; в этом смысле они представляю
т собой «почти решения».\n\nВсе решения ва
риационных уравнений заведомо являются
стационарными точками внутренних интег
ральных функционалов в соответствующих
классах почти решений. В зависимости от
ситуации стационарными точками таких фу
нкционалов могут быть не только решения.
Однако если почти решение уравнений Эйл
ера — Лагранжа склеено из нехарактерист
ических начально-краевых условий\, оно я
вляется стационарной точкой соответств
ующего внутреннего функционала тогда и
только тогда\, когда оно является решени
ем.\n\nВ этой связи удаётся также сформули
ровать соответствующую версию теоремы Н
ётер\, согласно которой всякая симметрия
вариационных уравнений либо определяет
законы сохранения\, либо порождает внут
ренние интегральные функционалы.\n\nПред
лагаемая конструкция служит ответом на
вопрос о том\, почему внутренняя геометр
ия вариационных уравнений знает об их ва
риационной природе: функционал действие
всегда воспроизводит себя внутри соотв
етствующих уравнений с помощью порождае
мого им внутреннего функционала.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM SB RAS\, Krasnoyark\, Russia)
DTSTART:20231005T110000Z
DTEND:20231005T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/60
DESCRIPTION:Title: Solutions of some wave models of mechanics\nby Oleg Kaptsov (I
CM SB RAS\, Krasnoyark\, Russia) as part of Mathematical models and integr
ation methods\n\n\nAbstract\nThe paper deals with one-dimensional nonstati
onary second order partial derivative equations describing waves in inhomo
geneous and nonlinear media.\n\nContact transformations and differential E
uler substitutions are used to construct solutions.\n\nGeneral solutions o
f some nonstationary models of continuum mechanics are found.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Borovskikh\, K.S. Platonova (MSU\, Moscow\, Russia)
DTSTART:20231019T110000Z
DTEND:20231019T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/61
DESCRIPTION:Title: Group analysis of the one-dimentional kinetic equation and the pro
blem of closing the moment system\nby A.V. Borovskikh\, K.S. Platonova
(MSU\, Moscow\, Russia) as part of Mathematical models and integration me
thods\n\n\nAbstract\nThe report is devoted to a problem that goes back to
the works of Maxwell and Clausius\, the relationship between the kinetic e
quations of the particles of the medium and the macroscopic characteristic
s of the medium. In the modern form\, the question is how to obtain the eq
uations of a continuum media from the kinetic equations. The fundamental p
roblem is the following: integration of the kinetic equation with power-la
w weights over velocities gives an infinite system of equations\, the firs
t of which are very similar to the equations of a continuous medium. But t
he system of equations of a continuous medium is finite. This means that t
he infinite system must be truncated and closed. The problem consists of t
wo questions: where to truncate and what ratio use to close. The report wi
ll present an approach based on group methods. The idea is to calculate th
e symmetry group of the kinetic equation\, transfer its action to macrosco
pic quantities\, find invariants already in terms of macroscopic quantitie
s\, and use them to construct a closure. This was successfully implemented
in the one-dimensional case\, the details will be presented in the report
.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov\, S.V. Mironov (Institute for physics of microstructu
res RAS\, Nizhny Novgorod\, Russia)
DTSTART:20231102T110000Z
DTEND:20231102T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/62
DESCRIPTION:Title: Sedeonic generalization of hydrodynamic equations. Vortex models
of plane turbulent walls-bounded flows\nby V.L. Mironov\, S.V. Mironov
(Institute for physics of microstructures RAS\, Nizhny Novgorod\, Russia)
as part of Mathematical models and integration methods\n\n\nAbstract\nWe
discuss a generalization of hydrodynamic equations based on the anticommut
ative spacetime\nalgebra of 16-component sedeons. A symmetric system of Ma
xwell-type equations is\nobtained\, which describes the longitudinal motio
n and rotation of vortex tubes. Based on these\nequations\, a simple model
of a plane\, fully developed turbulent flow is proposed. As examples\,\nw
e consider turbulent near-wall flows\, as well as Couette and Poiseuille f
lows in rectangular\nchannels.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Shmidt (Institute of computational modelling SB RAS\, Krasnoy
arsk\, Russia)
DTSTART:20231116T110000Z
DTEND:20231116T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/63
DESCRIPTION:Title: Approximate solution to a model of the far momentumless turbulent
wake\nby A.V. Shmidt (Institute of computational modelling SB RAS\, Kr
asnoyarsk\, Russia) as part of Mathematical models and integration methods
\n\n\nAbstract\nThe flow in the far momentumless turbulent wake is describ
ed with the use of a mathematical model based on the Rodi’s algebraic mo
del of Reynolds stresses. Similarity reduction of the model to a system of
ordinary differential equations is obtained. Asymptotic expansion of a so
lution in the vicinity of a singular point is used to construct approximat
e solution of the corresponding boundary value problem.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Broadbridge (La Trobe University\, Australia and IMI-Kyushu U
niversity\, Japan)
DTSTART:20231130T110000Z
DTEND:20231130T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/64
DESCRIPTION:Title: Reaction-diffusion models for fish populations with realistic mobi
lity\nby Phil Broadbridge (La Trobe University\, Australia and IMI-Kyu
shu University\, Japan) as part of Mathematical models and integration met
hods\n\n\nAbstract\nNonlinear reaction-diffusion equations\, with Fisher l
ogistic growth and constant diffusion coefficient\, have been used in fish
eries research to estimate sustainable harvesting rates and critical domai
n sizes of no-take areas. However\, constant diffusivity in a population d
ensity corresponds to standard Brownian motion of individuals\, with a nor
mal distribution for displacement over a fixed time interval. For availabl
e good data sets on mobile fish populations\, the distribution is certainl
y not normal. The data can be fitted with a long-tailed Lévy distribution
that corresponds to diffusion by fractional Laplacian.\n\nWe have develop
ed exact solutions for realistic Fisher-Kolmogorov-Petrovski-Piscounov mo
dels with diffusion by fractional Laplacian. These can also account for a
delay in the reaction term. It is then shown how to modify critical domain
sizes of protected areas.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ranis Ibragimov (Mathematics & Computer Science\, De Gruyter\, Bos
ton\, MA\, USA)
DTSTART:20231214T123000Z
DTEND:20231214T133000Z
DTSTAMP:20260404T111326Z
UID:mmandim/65
DESCRIPTION:Title: Invariant Solutions of Nonlinear Mathematical Modeling of Natural
Phenomena\nby Ranis Ibragimov (Mathematics & Computer Science\, De Gru
yter\, Boston\, MA\, USA) as part of Mathematical models and integration m
ethods\n\n\nAbstract\nThe main objective is to demonstrate the advantages
of the invariance method in obtaining new exact analytic solutions express
ed in terms of elementary functions for various physical phenomena. As one
particular application of the invariance method will be the mathematical
modeling of oceanic and atmospheric whirlpools causing weather instabiliti
es and\, possibly\, linked with climate change. As another particular exam
ple\, it will be demonstrated that the invariance method allows to obtain
the exact solutions of fully nonlinear Navier-Stokes equations within a th
in rotating atmospheric shell that serves as a simple mathematical descrip
tion of an atmospheric circulation caused by the temperature difference be
tween the equator and the poles with included equatorial flows modeling he
at waves\, known as Kelvin Waves. Special attention will be given to analy
zing and visualizing the conserved densities associated with obtained exac
t solutions. As another modeling scenario\, the exact solution of the shal
low water equations simulating equatorial atmospheric waves of planetary s
cales will be analyzed and visualized.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov\, S.V. Mironov (Institute for physics of microstructu
res RAS\, Nizhny Novgorod\, Russia)
DTSTART:20231228T110000Z
DTEND:20231228T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/66
DESCRIPTION:Title: Sedeonic equations of electromagnetic field. On the question of sy
mmetry between electricity and magnetism\nby V.L. Mironov\, S.V. Miron
ov (Institute for physics of microstructures RAS\, Nizhny Novgorod\, Russi
a) as part of Mathematical models and integration methods\n\n\nAbstract\nW
e reformulate the equations of the electromagnetic field in highly symmetr
ic form based on the space-time algebra of sedeons. The role of the Lorent
z gauge condition is discussed in detail and a generalization of the gauge
(gradient) invariance of the electromagnetic field equations is carried o
ut. The electrodynamics of Dirac monopoles and Schwinger dyons is consider
ed and the dyonic model of charged particles is discussed.\n\n1. V.L. Miro
nov\, S.V. Mironov\, Sedeonic equations in field theory\, Advances in Appl
ied Clifford Algebras\, 30\, 44 1-26 (2020).\n\n2. V. L. Mironov\, S. V. M
ironov\, Sedeonic field equations for dyons\, Advances in Applied Clifford
Algebras\, 28(3)\, 64 1-17 (2018).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dorodnitsyn (Keldysh Institute of Applied Mathematics\, M
oscow\, Russia)
DTSTART:20240118T110000Z
DTEND:20240118T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/67
DESCRIPTION:Title: Symmetries and conservation laws for differential equations\, diff
erence equations and second-order delay ODEs\nby Vladimir Dorodnitsyn
(Keldysh Institute of Applied Mathematics\, Moscow\, Russia) as part of Ma
thematical models and integration methods\n\n\nAbstract\nThe report is dev
oted to operators identities for Lagrangian and the Hamiltonian\napproach
to the connection of symmetries of equations with conservation laws\, and
the Lagrandian\nidentity for equations which have no variational statement
. We consider also difference equations and\nODEs with retarded argument a
nd appropriate operators identities.\n\nThis is based on joint works with
Roman Kozlov\, Pavel Winternitz\, Sergey Meleshko and Evgenii Kaptsov.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В.В. Веденяпин\, Н.Н. Фимин\, В.М. Чечет
кин\, А.Г. Петров (ИПМ им. М.В. Келдыша РАН /
ИПМех им. А.Ю. Ишлинского РАН)
DTSTART:20240201T110000Z
DTEND:20240201T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/68
DESCRIPTION:Title: Уравнение Власова — Эйнштейна и точ
ки Лагранжа\nby В.В. Веденяпин\, Н.Н. Фими
н\, В.М. Чечеткин\, А.Г. Петров (ИПМ им. М.В. К
елдыша РАН / ИПМех им. А.Ю. Ишлинского РАН)
as part of Mathematical models and integration methods\n\n\nAbstract\nВ
классических работах (см. [1]) уравнения д
ля полей предлагаются без вывода правых
частей. Здесь мы даем вывод правых часте
й уравнений Максвелла и Эйнштейна в рамк
ах уравнений Власова — Максвелла — Эйнш
тейна из классического принципа наимен
ьшего действия [2-4]\, а также их гидродина
мических и Гамильтон — Якобиевых следст
вий [2-4]. Ускоренное расширение Вселенной
\, отмеченное Нобелевской премией по физ
ике в 2011 году\, вызывает пристальное вним
ание. Общепринятым объяснением сейчас я
вляется добавление лямбда-члена Эйнштей
на в релятивистское действие. И хорошо и
звестно\, что в нерелятивистской теории
это соответствует добавлению отталкива
ющего квадратичного потенциала [2-4]. Мы и
зучаем решение типа Фридмана [2-4] (модель
Милна — Маккри) и точки Лагранжа с таким
потенциалом [4].\n\n1. Фок В.А. Теория простр
анства\, времени и тяготения. М.: ЛКИ\, 2007.\n
\n2. Веденяпин В.В.\, Воронина М.Ю.\, Руссков
А.А. О выводе уравнений электродинамики
и гравитации из принципа наименьшего де
йствия. Доклады РАН\, 2020\, том 495\, с. 9–13.\n\n3
. V.V. Vedenyapin\, N.N. Fimin\, V.M. Chechetkin. The generalized Friedman
model as a self–similar solution of Vlasov–Poisson equations system /
/ European Physical Journal Plus\, 136\, No 670 (2021).\n\n4. В.В. Ве
деняпин\, В.И. Паренкина\, А.Г. Петров\, Чжа
н Хаочэнь. Уравнение Власова — Эйнштейн
а и точки Лагранжа // Препринты ИПМ им. М.В
.Келдыша. 2022. № 23\, 23 с.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Велисевич (Сибирский федеральны
й университет)
DTSTART:20240215T110000Z
DTEND:20240215T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/69
DESCRIPTION:Title: Обратные задачи для эллиптических у
равнений и уравнений соболевского типа\nby А.В. Велисевич (Сибирский федеральны
й университет) as part of Mathematical models and integration
methods\n\n\nAbstract\nРассматриваются три обратн
ые задачи отыскания неизвестной функции
и неизвестного младшего коэффициента в
эллиптическом уравнении с граничными да
нными различного типа и интегральным ус
ловием переопределения на границе иссле
дуемой области. Также исследуются услов
ия стабилизации сильного решения обратн
ой задачи для уравнения соболевского ти
па к решению одной из этих задач. Операто
р 𝑀 предполагается сильно эллиптически
м и самосопряженным.\n\nОсновными результ
атами работы являются теоремы существов
ания и единственности сильного обобщенн
ого решения исходных задач\, а также дост
аточные условия непрерывной зависимост
и решений этих задач от исходных данных.
Кроме того\, к основным результатам отно
сятся достаточные условия стабилизации
сильного решения обратной задачи для ур
авнения соболевского типа к сильному ре
шению соответствующей стационарной обр
атной задачи для эллиптического уравнен
ия с интегральным условием переопределе
ния на границе.\n\nСуществование и единст
венность доказываются методом\, суть кот
орого состоит в продолжении данных с гра
ницы в область и сведении обратной задач
и к операторному уравнению второго рода\
, для неизвестного коэффициента.\n\nПракт
ический интерес к данным задачам обусло
влен тем фактом\, что в многочисленных пр
иложениях коэффициенты исходного уравн
ения характеризуют физические свойства
среды: проницаемость\, теплопроводность
и так далее. В рассмотренных задачах неи
звестным является коэффициент поглощен
ия.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Боровских (МГУ)
DTSTART:20240229T110000Z
DTEND:20240229T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/70
DESCRIPTION:Title: Геометрия группы Ли в групповом ана
лизе одномерного кинетического уравнен
ия\nby А.В. Боровских (МГУ) as part of Mathematical mo
dels and integration methods\n\n\nAbstract\nГрупповая класс
ификация одномерных кинетических уравн
ений (о которой рассказывалось в прошлом
докладе) и которая выполнялась с целью и
сследования возможности установления с
вязи между кинетическими уравнениями и
уравнениями сплошной среды с использова
нием группового подхода\, помимо уравнен
ий с максимальной ($8$-мерной) группой сим
метрий\, которые эквивалентны уравнению
с отсутствующим внешним силовым полем\,
дала еще ряд уравнений с субмаксимальны
ми группами симметрий (размерности три).
Эти уравнения связаны с весьма экзотиче
скими силовыми полями\, рассмотрение кот
орых можно было бы считать малоинтересн
ым с точки зрения приложений\, если бы гр
уппы симметрий в самых экзотических слу
чаях не оказались бы в точности совпадаю
щими с группами движений двумерных (в пр
остранстве переменных ($t$\, $x$)) римановых
метрик постоянной кривизны.\n\nЭто постав
ило вопрос о том\, какова геометрическая
сторона полученной классификации? Что э
то означает с геометрической точки зрен
ия? Попытки усмотреть какие-то геометрич
еские интерпретации в остальных субмакс
имальных случаях успеха не имели до тех
пор\, пока рассмотрения велись в простра
нстве переменных ($t$\, $x$). Помог здесь дос
таточно странный\, с точки зрения физики\
, сдвиг исходных позиций\, состоящий в то
м\, что геометрия стала рассматриваться
не в двумерном\, а в трехмерном пространс
тве ($t$\, $x$\, $c$)\, включающем\, помимо прежн
их переменных — времени и координаты —
еще и скорость.\n\nТакой ход позволил совс
ем по-другому взглянуть на геометрию. По
скольку размерность рассматриваемого п
ространства переменных оказалась совпа
дающей с размерностью группы\, искомая г
еометрия автоматически оказывалась и ге
ометрией самой группы. То есть речь пошл
а уже о том\, возможно ли на самой группе
Ли задать риманову геометрию так\, чтобы
она была инвариантна относительно этой
группы? Ответ оказался положительный и п
ростой\, такая геометрия задавалась\, как
выяснилось\, квадратичной формой с пост
оянными коэффициентами от $n$ линейных ди
фференциальных форм\, инвариантных отно
сительно той же группы. При этом оказало
сь\, что для любой такой квадратичной фор
мы (для любых коэффициентов) траектории
частиц в пространстве переменных ($t$\, $x$\,
$c$) являются спиралями\, то есть имеют по
стоянную кривизну и кручение. Основную ж
е роль в обосновании этого факта сыграла
алгебра\, которая была названа двойстве
нной\, и которая определяется условием к
оммутации с исходной алгеброй. Траектор
ии частиц\, которые были упомянуты выше\,
оказываются траекториями однопараметри
ческих подгрупп этой двойственной алгеб
ры\, и тот факт\, что эти траектории являю
тся спиралями\, порождает массу вопросов
об отношении этой геометрии к геометрич
еским конструкциям Э. Картана\, который п
олагал траектории однопараметрических
групп геодезическими.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM SB RAS\, Krasnoyark\, Russia)
DTSTART:20240314T110000Z
DTEND:20240314T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/71
DESCRIPTION:Title: Intermediate systems and invariants\nby Oleg Kaptsov (ICM SB R
AS\, Krasnoyark\, Russia) as part of Mathematical models and integration m
ethods\n\n\nAbstract\nIn this report some classical and new methods of int
egration of partial differential equations are considered. The approaches
of Monge and Darboux are briefly described. Examples of the construction o
f general solutions of second order equations based on invariants of the c
haracteristics of hyperbolic equations are given. Intermediate systems of
partial derivative equations are introduced in terms of differential algeb
ra. Equations possessing intermediate systems are found.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Вячеслав Кузоватов (Сибирский федер
альный университет)
DTSTART:20240321T110000Z
DTEND:20240321T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/72
DESCRIPTION:Title: Дзета-функция корней некоторого кла
сса целых функций и ее свойства\nby Вяче
слав Кузоватов (Сибирский федеральный у
ниверситет) as part of Mathematical models and integration metho
ds\n\n\nAbstract\nВ докладе будет рассмотрена дз
ета-функция Римана и способ получения фу
нкционального соотношения для нее\, осно
ванный на интегральных представлениях:
классической формуле Плана и интегральн
ом представлении Бине. Будет введено обо
бщение дзета-функции Римана\, а именно дз
ета-функция корней некоторого класса це
лых функций\, указана связь с классическ
ой дзета-функцией Римана.\n\nОсновным рез
ультатом доклада являются интегральные
представления для дзета-функции корней\,
аналог формулы Плана и формулы Бине. Отк
рытая задача: функциональное уравнение
для дзета-функции корней\, аналогичное ф
ункциональному уравнению для дзета-функ
ции Римана.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В.Л. Миронов\, С.В. Миронов (Институт ф
изики микроструктур РАН\, Нижний Новгоро
д)
DTSTART:20240404T110000Z
DTEND:20240404T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/73
DESCRIPTION:Title: Седеонные уравнения для полей с мас
сой кванта\, не равной нулю. Модель барио
н-барионного взаимодействия\nby В.Л. Мир
онов\, С.В. Миронов (Институт физики микро
структур РАН\, Нижний Новгород) as part of Mathem
atical models and integration methods\n\n\nAbstract\nНа основе п
ространственно-временной алгебры седео
нов сформулированы симметричные уравне
ния для полей с ненулевой массой кванта.
Рассматривается обобщение калибровочно
й (градиентной) инвариантности уравнени
й с учетом ненулевой массы кванта. Обсуж
дается модель взаимодействия точечных б
арионов.\n\n1. V. L. Mironov\, S. V. Mironov. Sedeonic equations in
field theory\, Advances in Applied Clifford Algebras\, 30\, 44 1-26 (2020
).\n\n2. S. V. Mironov\, V. L. Mironov. Sedeonic equations of massive fiel
ds // International Journal of Theoretical Physics\, 54(1)\, 153–168 (20
15).\n\n3. V. L. Mironov\, S. V. Mironov. Gauge invariance of sedeonic equ
ations for massive and massless fields\, International Journal of Theoreti
cal Physics\, 55\, 3105 (2016).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics)
DTSTART:20240418T110000Z
DTEND:20240418T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/74
DESCRIPTION:Title: Negative symmetries: properties and applications\nby V.E. Adle
r (Landau Institute for Theoretical Physics) as part of Mathematical model
s and integration methods\n\n\nAbstract\nOne of the definitions of negativ
e symmetry of an integrable equation is given by the formula $u_t=(R-a)^{-
1}(0)$ where $R$ is the recursion operator and $a$ is a parameter. This ex
tension of symmetry algebra is of interest from different points of view:
1) negative symmetry can be interesting as an independent equation\; 2) it
contains information about the entire integrable hierarchy\, since the ex
pansion in parameter a serves as a generating function for higher symmetri
es\; 3) there are applications in the problem of constructing finite-dimen
sional reductions\, especially in combination with classical symmetries (w
hich provides an approach to constructing solutions expressed through high
er analogues of Painlevé transcendents)\; 4) there are connections with o
ther constructions\, such as squared eigenfunctions symmetries and Bäcklu
nd transformations. In the talk\, we consider examples related to the KdV\
, Boussinesq and Krichever-Novikov equations and the Volterra lattice.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics)
DTSTART:20240425T110000Z
DTEND:20240425T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/75
DESCRIPTION:Title: Negative symmetries: properties and applications. Continuation\, p
art 2\nby V.E. Adler (Landau Institute for Theoretical Physics) as par
t of Mathematical models and integration methods\n\n\nAbstract\nOne of the
definitions of negative symmetry of an integrable equation is given by th
e formula $u_t=(R-a)^{-1}(0)$ where $R$ is the recursion operator and $a$
is a parameter. This extension of symmetry algebra is of interest from dif
ferent points of view: 1) negative symmetry can be interesting as an indep
endent equation\; 2) it contains information about the entire integrable h
ierarchy\, since the expansion in parameter a serves as a generating funct
ion for higher symmetries\; 3) there are applications in the problem of co
nstructing finite-dimensional reductions\, especially in combination with
classical symmetries (which provides an approach to constructing solutions
expressed through higher analogues of Painlevé transcendents)\; 4) there
are connections with other constructions\, such as squared eigenfunctions
symmetries and Bäcklund transformations. In the talk\, we consider examp
les related to the KdV\, Boussinesq and Krichever-Novikov equations and th
e Volterra lattice.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов (Институт математики
с вычислительным центром\, Уфа\, Россия)
DTSTART:20240523T110000Z
DTEND:20240523T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/76
DESCRIPTION:Title: Мероморфность решений системы урав
нений типа Пенлеве 34\, связанной с негати
вными симметриями уравнения Кортевега
— де Вриза\nby Б.И. Сулейманов (Институт
математики с вычислительным центром\, Уф
а\, Россия) as part of Mathematical models and integration methods\
n\n\nAbstract\nДоклад посвящен доказательству
того факта\, что при $t\\neq 0$ все локально г
оломорфные решения системы ОДУ\n$$(y_j)'''_{xxx
}=S_j(x\,t\,y_j\, u\,(y_j)'_x\, u'_x)=2u'_xy_j+4(u-\\lambda_j)(y_j)'_x\,\\
\; (j=1\, \\dots\,n)\,$$\nгде $u=\\dfrac{x}{6t}+\\dfrac{1}{3t}\\sum_{j=
1}^n y_j$ мероморфно продолжимы на всю компл
ексную плоскость изменения переменной $x
$. Данная система ОДУ при $n=1$ эквивалентн
а уравнению Пенлеве 34 (которое\, в свою оч
ередь\, выражается через решения второго
уравнения Пенлеве). Она была введена в р
ассмотрение в недавней статье V.$\\\,$E. Adler\,
M.$\\\,$P. Kolesnikov\, JMP\, 2023. Ей и её связям с нега
тивными симметриям была посвящена часть
предыдущего доклада В.$\\\,$Э. Адлера на да
нном семинаре.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. О. Смирнов (Санкт-Петербургский го
сударственный университет аэрокосмичес
кого приборостроения)
DTSTART:20240530T110000Z
DTEND:20240530T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/77
DESCRIPTION:Title: Различия между решениями скалярных
и векторных интегрируемых нелинейных ур
авнений с точки зрения теории конечнозо
нного интегрирования\nby А. О. Смирнов (С
анкт-Петербургский государственный уни
верситет аэрокосмического приборострое
ния) as part of Mathematical models and integration methods\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov (Institute for physics of microstructures RAS\, Nizhn
y Novgorod\, Russia)
DTSTART:20240919T090000Z
DTEND:20240919T100000Z
DTSTAMP:20260404T111326Z
UID:mmandim/78
DESCRIPTION:Title: Self-consistent hydrodynamic model of plasma. Sound waves in plasm
a\nby V.L. Mironov (Institute for physics of microstructures RAS\, Niz
hny Novgorod\, Russia) as part of Mathematical models and integration meth
ods\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irk
utsk\, Russia)
DTSTART:20241003T110000Z
DTEND:20241003T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/79
DESCRIPTION:Title: Traveling Alfven waves in plasma flows along magnetic field\nb
y S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irkutsk\,
Russia) as part of Mathematical models and integration methods\n\n\nAbstr
act\nIn the framework of ideal magnetohydrodynamics\, a one-dimensional pr
oblem of linear Alfven waves propagation is considered in a stationary flo
w of inhomogeneous plasma along straight uniform magnetic field. Four fami
lies of flows are found\, in which accelerated and retarded by the flow wa
ves of arbitrary shape can propagate independently of each other\, that is
\, without reflection. It is shown that in two of these families both wave
s have a similar structure\, but in the other two their structures differ
significantly.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.P. Tsarev (SFU\, Krasnoyarsk\, Russia)
DTSTART:20241017T110000Z
DTEND:20241017T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/80
DESCRIPTION:Title: Sparse recovery and Compressive sensing in theory and in practice<
/a>\nby S.P. Tsarev (SFU\, Krasnoyarsk\, Russia) as part of Mathematical m
odels and integration methods\n\n\nAbstract\nIn the 1990's\, algorithms fo
r solving linear systems with the number of equations smaller than the num
ber of unknowns\, provided that among the unknowns there are only a small
number of non-zero ones (however\, we do not know which of them are non-ze
ro!) were proposed.\n\nA new stage was opened in the early 2000's by the w
ell-known specialist in signal processing David Donoho and the Fields Meda
l winner Terence Tao and their students. The results in this area were awa
rded the 2018 Gauss Prize (given by the International Mathematical Union)\
, they were reported as plenary talks at the International Congress of Mat
hematicians\, etc.\n\nAfter the works of Donoho\, Tao and many other resea
rchers\, progress in this area was rapid. This research area was called "c
ompressive sensing" or "compressed sensing" (along with the older name "sp
arse recovery").\n\nThe most well-known applications of these results are
in signal processing. Particularly noteworthy are applications of sparse r
ecovery technologies in magnetic resonance imaging (MRI)\, which reduce th
e time spend by patients in the MRI machine and improve the quality of the
resulting image.\n\nThe report will discuss the main ideas of this area a
nd demonstrate a small practical application in the problem of finding jum
ps in a noisy signal.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. B. Borisov and D. V. Dolgikh (M.N. Mikheev Institute of Metal P
hysics of Ural Branch of Russian Academy of Sciences\, Yekaterinburg\, Rus
sia)
DTSTART:20241031T110000Z
DTEND:20241031T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/81
DESCRIPTION:Title: Symmetries of the classical Heisenberg model\nby A. B. Borisov
and D. V. Dolgikh (M.N. Mikheev Institute of Metal Physics of Ural Branch
of Russian Academy of Sciences\, Yekaterinburg\, Russia) as part of Mathe
matical models and integration methods\n\n\nAbstract\nThe symmetries of th
e classical Heisenberg model are examined. It is shown that such symmetrie
s are groups of conformal transformations and rotations. The invariance of
vortex structures with respect to a group of rotations is studied. The ap
plication of the found transformations of the group of field rotations to
the already known solutions of the Heisenberg model (such as instantons\,
vortex “targets” and “spirals”) generates other structures\, which
are also solutions of this model\, with the properties being determined b
y the original structures.\n\nKeywords: Heisenberg model\, ferromagnet\, v
ortex\, Lee groups\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov
DTSTART:20241114T110000Z
DTEND:20241114T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/82
DESCRIPTION:Title: Integration of acoustic wave equations for inhomogeneous media\nby O. V. Kaptsov as part of Mathematical models and integration method
s\n\n\nAbstract\nWe obtain exact solutions of the acoustic wave equations
for inhomogeneous media. Two methods for integrating these equations are p
roposed. The first one is based on the of the Laplace cascade method\, whi
le the second method involves reducing two-dimensional and three-dimension
al models to the wave equation. In the case of plane waves\, we find new s
olutions depending on two arbitrary functions. These solutions generalize
the classical ones obtained by Euler. In the two-dimensional and three-di
mensional cases\, equations that can be reduced to equations with constant
coefficients are found.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia)
DTSTART:20241128T110000Z
DTEND:20241128T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/83
DESCRIPTION:Title: Maxwell's and Stokes' operators associated with elliptic different
ial complexes\nby A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia) as pa
rt of Mathematical models and integration methods\n\n\nAbstract\nWe propos
e a regular method for generating consistent systems of partial differenti
al equations (PDEs) that describe a wide class of models in natural scienc
es. Such systems appear within typical constructions of the Homological Al
gebra as complexes of differential operators describing compatibility cond
itions for overdetermined PDEs. Additional assumptions on the ellipticity/
parameter-dependent ellipticity of the differential complexes provide a w
ide range of elliptic\, parabolic and hyperbolic operators. In particular\
, most equations related to modern Mathematical Physics are generated by t
he de Rham complex of differentials on exterior differential forms. These
includes the equations based on elliptic Laplace and Lam\\'e type operator
s\; the parabolic heat and mass transfer equations\; the Euler type and Na
vier-Stokes type equations in Hydrodynamics\; the hyperbolic wave equation
and the Maxwell equations in Electrodynamics\; the Klein-Gordon equation
in Relativistic Quantum Mechanics\; and so on. The advantage of our approa
ch is that this generation method covers a broad class of generating syste
ms\, especially in high dimensions\, due to different underlying algebraic
structures than the conventional ones.\n\nThis is joint work with V. L. M
ironov and A. N. Polkovnikov.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Nazarenko (Université de Nice Sophia Antipolis: Nice\, Prov
ence-Alpes-Cote d'Azur\, France)
DTSTART:20241212T110000Z
DTEND:20241212T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/84
DESCRIPTION:Title: Universal regimes of turbulence in Bose-Einstein condensation\
nby S. V. Nazarenko (Université de Nice Sophia Antipolis: Nice\, Provence
-Alpes-Cote d'Azur\, France) as part of Mathematical models and integratio
n methods\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. В. Боровских (МГУ\, Россия)
DTSTART:20241226T110000Z
DTEND:20241226T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/85
DESCRIPTION:Title: Метод распространяющихся волн для о
дномерной неоднородной среды с памятью\nby А. В. Боровских (МГУ\, Россия) as part of Mathe
matical models and integration methods\n\n\nAbstract\nДля уравне
ния $u_{tt}=u_{xx}$ имеется три канонических сп
особа представления общего решения:\n\n—
через распространяющиеся волны $u=f(x-t)+g(x+t
)$\;\n\n— формула Даламбера (интеграл от на
чальных данных)\;\n\n— в виде ряда Фурье.\n\n
Второй и третий способы были распростра
нены на очень широкие классы уравнений.
В наиболее абстрактном исполнении метод
Фурье сейчас представлен в спектрально
й теории операторов в различных функцио
нальных пространствах\, а интегральное п
редставление — в виде теории полугрупп.
Что же касается первого способа\, то он т
ак и остался исключительной принадлежно
стью простейшего уравнения\, хотя даже д
ля такого уравнения\, как только область\
, в которой оно задано\, оказывается не пр
ямоугольной\, или краевые условия не про
стейшие (Дирихле/Нейман) мы немедленно в
озвращаемся к формуле распространяющих
ся волн. Это порождает естественный вопр
ос\, нельзя ли построить метод распростр
аняющихся волн в более общем варианте?\n\n
Оказывается\, ответ на этот вопрос являе
тся положительным\, по крайней мере в одн
омерном случае. В докладе будет дано пре
дставление общего решения для волнового
уравнения для неоднородной струны и для
уравнения в одномерной неоднородной ср
еде с памятью через распространяющиеся
волны. Основной неожиданностью метода р
аспространяющихся волн здесь является т
о\, что эти волны не являются решением ис
ходного уравнения. Решение получается т
олько как сумма. Это объясняет относител
ьную неуспешность известных методов пои
ска решений типа волны в неоднородной ср
еде — каждый раз волны предполагались р
ешением исходного уравнения.\n\nОбзор эти
х результатов представлен в статье:\n\nБо
ровских А.В. Метод распространяющихся во
лн // Дифференциальные уравнения. - 2023. - Т.
59. - №5. - C. 619-634. doi: 10.31857/S0374064123050060 (полный
текст см. https://istina.msu.ru/download/557753070/1tEucw:8EoRHDe8U
C1jm1QVRz4x9QKRDM4/ )\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov (Institute for physics of microstructures RAS\, Nizhn
y Novgorod\, Russia)
DTSTART:20250123T110000Z
DTEND:20250123T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/86
DESCRIPTION:Title: Modified equations of heat transfer and diffusion in solids\nb
y V.L. Mironov (Institute for physics of microstructures RAS\, Nizhny Novg
orod\, Russia) as part of Mathematical models and integration methods\n\n\
nAbstract\nWe discuss heat and mass transfer equations based on modified r
elationships for heat flux (Fourier's law) and diffusing impurity flux (Fi
ck's law). It is shown that the proposed modification leads to second-orde
r elliptic equations that describe the change in profiles of temperature a
nd impurity concentration with a finite velocity. One-dimensional heat tra
nsfer processes in plates are considered as an example.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. B. Karmanova (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20250206T110000Z
DTEND:20250206T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/87
DESCRIPTION:Title: Area Formula for Surfaces in Non-Holonomic Structures\nby M. B
. Karmanova (Sobolev Institute of Mathematics\, Novosibirsk\, Russia) as p
art of Mathematical models and integration methods\n\n\nAbstract\nNonholon
omic structures can be considered as a natural generalization of the struc
tures of Riemannian geometry. One of their main features is a specific met
ric\, relative to which one can traverse distances of different orders alo
ng different directions ($t$\, $t^2$\, $t^3$\, etc.) in time $t$. Therefor
e\, mappings that are Lipschitz in the classical sense are generally not s
uch in the nonholonomic sense\, and vice versa. Nevertheless\, in the seco
nd half of the 20th century\, the theory of sub-Riemannian differentiabili
ty was created\, which allows one to approximate "complicated" mappings by
regular ones. Carnot groups are one of the well-known examples of nonholo
nomic structures. The talk will discuss the sub-Riemannian analogue of the
area formula for surfaces obtained under intrinsically Lipschitz mappings
of open sets of Carnot groups. Such groups and their generalizations\, Ca
rnot manifolds\, arise naturally in both theoretical and applied fields\,
such as neurobiology\, robotics\, and astrodynamics.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Lopatin (Federal Research Center for Information and Computat
ional Technologies\, Novosibirsk\, Russia)
DTSTART:20250220T110000Z
DTEND:20250220T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/88
DESCRIPTION:Title: Model and bending analysis of sandwich beam with composite facings
and compressible orthotropic core using Abramov’s sweep method\nby
A.V. Lopatin (Federal Research Center for Information and Computational Te
chnologies\, Novosibirsk\, Russia) as part of Mathematical models and inte
gration methods\n\n\nAbstract\nModern sandwich structures are employed in
a broad range of aerospace\, marine and civil structural applications. The
y are efficient and lightweight constructions with high bending stiffness\
, high strength\, and high buckling resistance. Such modern sandwich struc
tures are combination of composite facings with a lightweight core layer.
The facings carry the tensile and compressive loads\, while the core trans
mits shear loads and serves to hold the facings in positions\, which maxim
ize the flexural stiffness of the structure. Therefore\, the general struc
tural response of a sandwich structure is an action\, consisting of couple
\, compression or tension stress resultants in the facings and shear stres
ses along with vertical normal stresses within the core. Note that\, in su
ch structures\, the facings may undergo different displacements due to the
compressible core that may change its height. Proper reflection of this e
ffect in the strain-stress analysis would require the application of the a
dvanced modeling and computational techniques and approaches.\n\nIn this s
tudy the new computational model of sandwich beam is developed. The beam o
ne-dimensional model by virtue of its relative simplicity is useful for pr
eliminary analyses of the more complicated two-dimensional sandwich struct
ures. The model for the facings was built based on the traditional hypothe
ses that allow a transverse shear deformation to be taken into account. Th
e deformation model created for the elastic orthotropic core is original.
This model considers a non-linear character of variation of the transverse
and axial displacements over the thickness of core. Governing system of d
ifferential equations\, describing join deformation of facings and core\,
was derived using static and kinematic contact conditions between these pa
rts of the structure. System of governing differential equations has 14th
order. Numerical analysis of the stress-strain state of the sandwich beam
for various loading cases and boundary conditions has been performed. Syst
em of differential equations\, together with the corresponding boundary co
nditions\, represented the boundary value problem that was solved using Ab
ramov’s sweep method. Finite element modeling of the sandwich beam was e
xecuted using the FEM software package MSC Nastran® and the results were
compared with the developed theory. The computational model of deformation
of the sandwich beam and method of its analysis developed in this study p
rovide an opportunity to investigate a strong oscillating behavior of the
components of stress-strain state of the structure under consideration. Th
is allows the results of analyses performed to be used for the verificatio
n of solutions for similar problems found using numerical techniques\, inc
luding the finite element method.\n\nThis is joint work with A.E. Burov (F
ederal Research Center for Information and Computational Technologies) and
E.A. Lopatin (Steklov Mathematical Institute of the Russian Academy of Sc
iences).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostya Druzhkov (Department of Mathematics and Statistics\, Univer
sity of Saskatchewan\, Saskatoon\, Canada)
DTSTART:20250306T123000Z
DTEND:20250306T133000Z
DTSTAMP:20260404T111326Z
UID:mmandim/89
DESCRIPTION:Title: Invariant reduction for partial differential equations: conservati
on laws\nby Kostya Druzhkov (Department of Mathematics and Statistics\
, University of Saskatchewan\, Saskatoon\, Canada) as part of Mathematical
models and integration methods\n\n\nAbstract\nAmong various methods for c
onstructing exact solutions of partial differential equations\, the symmet
ry approach is particularly noteworthy. It turns out that systems describi
ng invariant solutions inherit many invariant geometric structures\, even
in the case of higher symmetries. In the talk\, we will discuss how invari
ant conservation laws of systems with two independent variables give rise
to constants of invariant motion. The procedure involved is algorithmic fo
r systems of evolution equations.\n\nThis is joint work with Alexei Chevia
kov.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Meleshko (Suranaree University of Technology\, Nakhon Ratcha
sima\, Thailand)
DTSTART:20250320T110000Z
DTEND:20250320T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/90
DESCRIPTION:Title: Equivalence to the classical heat equation through reciprocal tran
sformations\nby S. V. Meleshko (Suranaree University of Technology\, N
akhon Ratchasima\, Thailand) as part of Mathematical models and integratio
n methods\n\n\nAbstract\nThis paper investigates the equivalence of parabo
lic partial differential equations to the classical\none-dimensional heat
equation using reciprocal transformations. The equations are assumed to be
autonomous\, and the methodology applied is similar to S. Lie’s approac
h to solving the linearization problem of second-order ordinary differenti
al equations. The research is structured in two main parts. In the first p
art\, necessary constraints on the class of parabolic partial differential
equations with two independent variables\, which are equivalent to the cl
assical heat equation under a reciprocal transformation\, are identified.
In the second part\, the remaining conditions are examined\, and sufficien
t conditions are derived. The corresponding differential equations are the
n obtained. All possible cases that arise are thoroughly analyzed\, and th
e theory is illustrated with several examples.\n\nThis is joint work with
P. Siriwat (Thailand) and S. R. Svirshchevskii (Russia).\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir L. Saveliev (Fesenkov Astrophysical Institute\, Almaty\,
Kazakhstan)
DTSTART:20250403T110000Z
DTEND:20250403T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/91
DESCRIPTION:Title: Kinetic equation of turbulence from the Boltzmann equation\nby
Vladimir L. Saveliev (Fesenkov Astrophysical Institute\, Almaty\, Kazakhs
tan) as part of Mathematical models and integration methods\n\n\nAbstract\
nWe have shown how the kinetic equation for the velocity distribution func
tion of an ensemble of turbulent velocities can be rigorously obtained fro
m the Boltzmann kinetic equation with the classical collision integral. Co
mpared to the Boltzmann equation on the left-hand side\, the resulting kin
etic equation of turbulence contains ten additional terms. Also\, instead
of the frequency of molecular collisions\, the collision integral in the k
inetic equation of turbulence includes the collision frequency\, which is
significantly less than the frequency of molecular collisions. There are t
wo key steps we have undertaken in obtaining the kinetic equation of turbu
lence. First\, we used the invariance of the collision integral of the Bol
tzmann equation with respect to the Gaussian transformations. Second\, we
introduced the idea of fragmentation of turbulent flows into turbulent flu
id quasiparticles. Each such quasiparticle is described by an equilibrium
distribution of molecular velocities with fluctuating mean velocity. Also\
, each quasiparticle is characterized by its size\, which is in the range
of length scales larger than the mean free path of molecules and less than
the typical length of spatial variation in the turbulence distribution fu
nction.\n\n[1] Phys. Fluids 36\, 125175 (2024)\; doi: 10.1063/5.0242731\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В. И. Кузоватов (Сибирский Федеральн
ый Университет)
DTSTART:20250417T110000Z
DTEND:20250417T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/92
DESCRIPTION:Title: Об одном обобщении формулы Бине\nby
В. И. Кузоватов (Сибирский Федеральный У
ниверситет) as part of Mathematical models and integration metho
ds\n\n\nAbstract\nКлассическая формула Бине выр
ажает значение логарифмической произво
дной $\\Gamma$-функции Эйлера через некоторо
е интегральное представление. Данный до
клад будет посвящен получению обобщения
данного результата. А именно\, получено
интегральное представление для логариф
мической производной целой функции коне
чного порядка (меньше $1/2$) с нулями\, кото
рые образуют некоторую последовательно
сть целых отрицательных чисел. Доказате
льство основано на использовании класси
ческой формулы суммирования Плана и реш
ении одной интерполяционной задачи. Пол
ученный результат может быть использова
н при получении функционального соотнош
ения для дзета-функции корней\, аналогич
ного функциональному уравнению для клас
сической дзета-функции Римана.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. V. Shmidt (Institute of computational modelling SB RAS\, Krasno
yarsk\, Russia)
DTSTART:20250430T110000Z
DTEND:20250430T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/93
DESCRIPTION:Title: About one method for solving boundary-value problems arising in fr
ee turbulence\nby A. V. Shmidt (Institute of computational modelling S
B RAS\, Krasnoyarsk\, Russia) as part of Mathematical models and integrati
on methods\n\n\nAbstract\nAn approximate solution of the boundary-value pr
oblem for a semi-empirical model of the far momentumless turbulent wake is
constructed matching asymptotic expansion of the solution at the boundary
of the wake with the power series expansion of the solution near its axis
. A value of the self-similarity parameter of the problem is determined du
ring matching procedure. Maximum error between constructed solution and nu
merical solution does not exceed $0.3\\\,\\%$.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Raskovalov (Institute of Metal Physics UB RAS\, Ekaterinburg\,
Russia)
DTSTART:20250515T110000Z
DTEND:20250515T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/94
DESCRIPTION:Title: Nonlinear excitations in magnets with a spiral and stripe domain s
tructure\nby A. Raskovalov (Institute of Metal Physics UB RAS\, Ekater
inburg\, Russia) as part of Mathematical models and integration methods\n\
n\nAbstract\nThe new analytical solutions of the basis magnetism models (t
he Landau–Lifshitz and sine-Gordon equations) are found. They describe q
uasi-one-dimensional solitons on the periodic background\, that is\, in th
e stripe domain structure of one- and two-axis ferromagnets and in the spi
ral structure of magnets without inversion center. The basis investigation
method is the “dressing technique” – modification of the inverse sc
attering problem\, based on the Riemann problem of functions of a complex
variable. The detailed analysis of the obtained solutions is presented. Th
e possibilities to excite and detect the solitons on the experiments are d
iscussed.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Kiselev (Intitute of Metal Physics UB RAS\, Ekaterinburg\, Russ
ia)
DTSTART:20250529T110000Z
DTEND:20250529T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/95
DESCRIPTION:Title: Nonlinear dynamics of the bulk magnetostatic and exhange-dipole mo
des in the ferromagnetic plate\nby V. Kiselev (Intitute of Metal Physi
cs UB RAS\, Ekaterinburg\, Russia) as part of Mathematical models and inte
gration methods\n\n\nAbstract\nEffective equations of the Davey-Stewartson
type are obtained by the multiscale expansion technique\, that describe e
volution of the three-dimensional magnetostatic excitations in the ferroma
gnetic plate. The proposed approach admits generalization. It is shown\, t
hat in the ferromagnetic plates with thickness more than the exchange leng
th evolution of the three-dimensional exchange-dipole wave packets is also
described by the Davey-Stewartson equations. The threshold values of inst
ability of the plane monochromatic waves are calculated. The modulational
instability of such waves leads to the formation of coherent structures.
The conditions of the formation and explicit solutions for plane soliton e
xcitations are found. In the framework of the proposed model\, the possibi
lity of the critical collapse of the space localized two-dimensional wave
structures is predicted.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Borisov (Institute of Metal Physics UB RAS\, Ekaterinburg\, Rus
sia)
DTSTART:20250612T110000Z
DTEND:20250612T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/96
DESCRIPTION:Title: Vortex lattices in two-dimensional ferromagnetics\nby A. Boris
ov (Institute of Metal Physics UB RAS\, Ekaterinburg\, Russia) as part of
Mathematical models and integration methods\n\n\nAbstract\nWe have integra
ted the two-dimensional Heisenberg model using classical differential geom
etry methods. Following a hodograph transformation\, the model equations h
ave been stated in terms of a metric tensor and its derivatives in a curvi
linear coordinate system. A general solution of the Heisenberg model in a
non-orthogonal coordinate system is found\, when the metric tensor depends
on two variables. New types of different vortex lattices in a two-dimensi
onal ferromagnet are predicted and analyzed.\n\nThis is joint work with D.
Dolgih.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. Kaptsov (FRC ICT\, Novosibirsk\, Russia)
DTSTART:20250925T110000Z
DTEND:20250925T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/97
DESCRIPTION:Title: Solutions to the equations of acoustics of inhomogeneous media and
gas dynamics\nby O. Kaptsov (FRC ICT\, Novosibirsk\, Russia) as part
of Mathematical models and integration methods\n\n\nAbstract\nThis paper c
onsiders one-dimensional equations of acoustics equations of inhomogeneous
media and the system of gas dynamics equations with constant entropy. Usi
ng the Riemann approach\, the gas dynamics equations are reduced to a seco
nd-order linear hyperbolic equation with variable coefficients. Solutions
to this equation are constructed using Euler–Darboux transformations. Th
is allows us to find new exact solutions of the equations of acoustics and
gas dynamics\, depending on two arbitrary functions.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosibirsk\
, Russia)
DTSTART:20251009T110000Z
DTEND:20251009T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/98
DESCRIPTION:Title: Nonlinear interaction of the cylinder with free boundaries and int
erfaces\nby N. Makarenko (Lavrentyev Institute of Hydrodynamics\, Novo
sibirsk\, Russia) as part of Mathematical models and integration methods\n
\n\nAbstract\nThe problem of unsteady motion of a cylinder in a deep ideal
fluid is considered. The reduction of the initial boundary value problem
for the Euler equations to a system of nonlinear boundary integral-differe
ntial equations is used. Asymptotic solutions are constructed\, that descr
ibe the early stage of a non-stationary flow that forms when a body accele
rates from rest.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. I. Kuzovatov (Siberian Federal University\, Krasnoyarsk\, Russi
a)
DTSTART:20251023T110000Z
DTEND:20251023T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/99
DESCRIPTION:Title: On determining the number of real zeros of a system of entire func
tions using computer algebra methods\nby V. I. Kuzovatov (Siberian Fed
eral University\, Krasnoyarsk\, Russia) as part of Mathematical models and
integration methods\n\n\nAbstract\nВ докладе речь пойде
т о создании инструментария для определ
ения числа вещественных нулей системы ц
елых функций многих комплексных перемен
ных. Методология исследования базируетс
я на том\, что\, при определенных ограниче
ниях\, число вещественных нулей такой си
стемы совпадает с числом вещественных н
улей ее результанта. В работе приводится
алгоритм\, вычисляющий число вещественн
ых нулей результанта системы. Для этого
вычисляются степенные суммы результант
а системы и исследуется ганкелева матри
ца\, составленная из них. Алгоритм реализ
ован в системе компьютерной алгебры Maple.
Преимущество предлагаемого подхода к на
хождению числа вещественных нулей систе
мы целых функций состоит в том\, что он по
зволяет определять это число\, не вычисл
яя самих нулей. Полученные результаты мо
гут найти применение в различных прикла
дных задачах\, например\, в задаче опреде
ления числа стационарных состояний сист
емы дифференциальных уравнений химичес
кой кинетики.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K. Druzhkov (University of Saskatchewan\, Saskatoon\, Canada)
DTSTART:20251106T123000Z
DTEND:20251106T133000Z
DTSTAMP:20260404T111326Z
UID:mmandim/100
DESCRIPTION:Title: General mechanism of invariant reduction and Noether's theorem\nby K. Druzhkov (University of Saskatchewan\, Saskatoon\, Canada) as par
t of Mathematical models and integration methods\n\n\nAbstract\nGiven a lo
cal (point\, contact\, or higher) symmetry of a system of partial differen
tial equations\, one can consider the system that describes the invariant
solutions (the invariant system). It seems natural to expect that the inva
riant system inherits symmetry-invariant geometric structures in a specifi
c way. We propose a mechanism of reduction of symmetry-invariant geometric
structures\, which relates them to their counterparts on the respective i
nvariant systems. This mechanism covers conservation laws\, the stationary
action principle\, presymplectic structures\, and more. In particular\, a
version of Noether's theorem naturally arises for systems that describe i
nvariant solutions.\n\nThis is joint work with A. Cheviakov.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irk
utsk\, Russia)
DTSTART:20251120T110000Z
DTEND:20251120T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/101
DESCRIPTION:Title: Traveling waves as solutions of factorized hyperbolic equation\nby S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irkut
sk\, Russia) as part of Mathematical models and integration methods\n\n\nA
bstract\nWe consider the solutions of a 1D linear factorized second-order
hyperbolic equation that describes the wave propagation in an inhomogeneou
s moving medium. The necessary and sufficient condition is found under whi
ch both waves propagate independently\, that is\, without reflection. Poss
ible variants of wave structure are described.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.M. Kamchatnov (Institute of Spectroscopy Russian Academy of Scie
nces\, Moscow\, Russia)
DTSTART:20251204T110000Z
DTEND:20251204T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/102
DESCRIPTION:Title: Asymptotic integrability of nonlinear wave equations\nby A.M.
Kamchatnov (Institute of Spectroscopy Russian Academy of Sciences\, Mosco
w\, Russia) as part of Mathematical models and integration methods\n\n\nAb
stract\nThe notion of asymptotic integrability is based on the asymptotic
theory of propagation of high-frequency wave packets along large-scale and
time-dependent backgrounds. We assume that the evolution of the backgroun
d obeys the dispersionless (hydrodynamic) limit of the nonlinear wave equa
tion under consideration and demand that the Hamilton equations for the pa
cket's propagation have an additional integral of motion independently of
the initial conditions for the background dynamics. This condition is stud
ied for systems described by one or two wave variables\, and it is shown t
hat it imposes strong restrictions on the dispersion relation for linear h
armonic waves in the case of two wave variables. Existence of the integral
of Hamilton’s equations leads to important consequences: (1) it allows
one to calculate the number of solitons produced from an intensive initial
pulse\; (2) this formula can be generalized in a natural way to the Bohr-
Sommerfeld quantization rule for parameters of solitons produced from such
a pulse\; (3) if the condition of asymptotic integrability is only fulfil
led approximately\, then the Bohr-Sommerfeld rule provides the solitons’
parameters with good accuracy even for not completely integrable equation
s\; (4) if it is fulfilled exactly\, then the appearing in the theory inte
gral can be identified with the quasiclassical limit of one of the equatio
ns of the Lax pair for the corresponding completely integrable equation wi
th the same dispersion relation and equations of the dispersionless limit\
, moreover\, the second equation of the Lax pair is related to the phase v
elocity of linear waves\; (5) “quantization” of the quasiclassical lim
it allows one to restore the full expressions for the Lax pair equations\;
(6) analytical continuation of the integral into the complex plane of wav
e numbers yields the expression for the soliton’s inverse half-width as
a function of the background wave variables\; (7) existence of such an int
egral for soliton motion leads to formulation of Hamiltonian dynamics of s
olitons moving along not-uniform and time-dependent background. The theory
is illustrated by examples\, and it is confirmed by comparison with numer
ical simulations.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Sitnik (Belgorod State University\, Russia)
DTSTART:20251218T110000Z
DTEND:20251218T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/103
DESCRIPTION:Title: On generalizations of discrete and integral Cauchy–Bunyakovsky
inequalities by the method of mean values. Some applications\nby S.M.
Sitnik (Belgorod State University\, Russia) as part of Mathematical models
and integration methods\n\n\nAbstract\nIn talk we consider generalization
s of discrete and integral Cauchy–Bunyakovsky inequalities by the method
of mean values with some applications. Mostly the material is compiled as
a short survey\, but some results are proved. Main results are listed\, i
ncluding an interesting inequality with maximum and minimum values. Some a
pplications are considered from different fields of mathematics. Among the
m are estimates for some special functions\, including Euler gamma and inc
omplete gamma function\, the Legendre complete elliptic integrals of the f
irst kind. Also some further possible generalizations are considered and o
utlined\, including generalizations of the Acz´el and Minkovskii inequali
ties\, a case of spaces with sign–indefinite form\, the Jackson’s 𝑞
-integrals\, and some others.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. N. Pelinovsky (International Laboratory of Dynamical Systems an
d Applications(HSE Nizhny Novgorod)\, Russia)
DTSTART:20260122T110000Z
DTEND:20260122T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/104
DESCRIPTION:Title: Soliton turbulence and rogue waves in systems described by Kortew
eg–de Vries type equations\nby E. N. Pelinovsky (International Labor
atory of Dynamical Systems and Applications(HSE Nizhny Novgorod)\, Russia)
as part of Mathematical models and integration methods\n\n\nAbstract\nС
олитонный газ (солитонная турбулентност
ь) является предметом интенсивных иссле
дований из-за его большой важности для м
ногих физических систем. Обычно этот тер
мин используется для интегрируемых моде
лей\, где солитоны взаимодействуют упруг
о. Однако солитонная турбулентность мож
ет быть также частью неинтегрируемой ди
намики\, где могут существовать долгожив
ущие решения в виде почти солитонов.\n\nВ
настоящем докладе представлены результ
аты по исследованию солитонной турбулен
тности в рамках уравнений типа Кортевег
а – де Вриза: как в интегрируемых моделя
х (классическое уравнение Кортевега – д
е Вриза\, модифицированное уравнение Кор
тевега – де Вриза\, уравнение Гарднера)\,
так и в рамках неинтегрируемых на пример
е уравнения Шамеля\, нелинейный член кот
орого содержит модуль волновой функции.
Некоторые важные статистические характ
еристики (функции распределения\, момент
ы и т. д.) рассчитаны численно для однопол
ярных и разнополярных солитонных газов.
Динамика однополярных газов оказалось о
чень похожей в случае интегрируемых и не
интегрируемых моделей. Однако неупругое
взаимодействие разнополярных солитоно
в приводит к передаче энергии от меньших
солитонов к большим в рамках неинтегрир
уемых моделей. С увеличением числа разно
полярных солитонов в волновой системе э
тот эффект передачи энергии от меньшего
солитона к большему\, а также возникнове
ние дисперсионных волн при каждом взаим
одействии солитонов приводит к существе
нному увеличению эксцесса (четвертого с
татистического момента)\, который в инте
грированных системах оставался бы квази
-стационарным. Демонстрируется возможно
сть образования аномально больших импул
ьсов в результате эволюции таких волнов
ых полей.\n\nThis is joint work with E. G. Didenkulova.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Mironov (Institute for physics of microstructures RAS\, Nizhny
Novgorod\, Russia)
DTSTART:20260205T110000Z
DTEND:20260205T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/105
DESCRIPTION:Title: Wind profiles in atmospheric boundary layer\nby V. Mironov (I
nstitute for physics of microstructures RAS\, Nizhny Novgorod\, Russia) as
part of Mathematical models and integration methods\n\n\nAbstract\nWe pro
pose an analytical algebraic model of a turbulent boundary layer based on
the equations for vortex flow\, which take longitudinal motion and rotatio
n of vortex tubes into account. In case of plane turbulent flows this mode
l allows one to calculate the mean velocity distributions in boundary laye
rs under various conditions. In particular\, we verify proposed model by c
omparison with the experimental profiles measured in the wind tunnel as we
ll as by fitting of experimental low-level jets profiles measured in atmos
pheric boundary layer. In all considered cases the calculated model profil
es demonstrate good agreement with experimental data.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. P. Kiselev (St. Petersburg Department of V.A.Steklov Institute
of Mathematics of the Russian Academy of Sciences)
DTSTART:20260219T110000Z
DTEND:20260219T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/106
DESCRIPTION:Title: Solutions of the wave equation with arbitrary functions: relative
ly undistorted waves\nby A. P. Kiselev (St. Petersburg Department of V
.A.Steklov Institute of Mathematics of the Russian Academy of Sciences) as
part of Mathematical models and integration methods\n\n\nAbstract\nSoluti
ons of the wave equation containing arbitrary functions have attracted the
attention of researchers since the 18th century to the present day. Four
such solutions and some of their applications will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov (Federal Research Center for Information and Computi
ng Technologies\, Novosibirsk\, Russia)
DTSTART:20260305T110000Z
DTEND:20260305T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/107
DESCRIPTION:Title: Solutions to three-dimensional steady-state gas dynamics equation
s\nby O. V. Kaptsov (Federal Research Center for Information and Compu
ting Technologies\, Novosibirsk\, Russia) as part of Mathematical models a
nd integration methods\n\n\nAbstract\nThis paper examines the three-dimens
ional stationary equations of a polytropic gas and employs symmetry method
s to construct exact analytical solutions. In the Chaplygin gas case\, the
analysis yields a highly general solution family depending on three arbit
rary functions\, while the general adiabatic index formulation admits expl
icit solutions parameterized by several constants.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.E. Kulagin (Tomsk Polytechnic University\, Tomsk\, Russia. V.E.
Zuev Institute of Atmospheric Optics\, Tomsk\, Russia.)
DTSTART:20260326T110000Z
DTEND:20260326T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/108
DESCRIPTION:Title: Solutions to the nonlinear Schrodinger equation with an anti-Herm
itian term\, localized on curves\, and quasi steady vortex states\nby
A.E. Kulagin (Tomsk Polytechnic University\, Tomsk\, Russia. V.E. Zuev Ins
titute of Atmospheric Optics\, Tomsk\, Russia.) as part of Mathematical mo
dels and integration methods\n\n\nAbstract\nSpeaking about semiclassically
localized solutions to the Schrödinger equation\, we mean the class of a
symptotic solutions that are obtained for the linear Schrödinger equation
by the Maslov complex germ method [1\,2\,3]. Such solutions are localized
in a neighbourhood of the trajectory in the phase space (point for any fi
xed time) that is determined by solutions to the Hamilton system (classica
l equations). Such approach was also generalized for nonlinear equations [
4].\nIn our report\, we consider the Cauchy problem where the solutions to
the Schrödinger equation with a nonlocal nonlinearity are localized in a
neighborhood of the evolving curve. Also\, we add the anti-Hermitian term
s that allows us to consider the dissipative effects. Such problem is solv
ed using the transition to the space of variables of higher dimension\, wh
ere we can apply elements of the Maslov complex germ method. Asymptotic so
lutions to the original problem are the projection of the solutions in the
extended space to the original space. The formalism proposed becomes appl
icable to the problem of the vortex lattice formation in condensed media w
ith collective excitations. It is shown that such process includes the sem
iclassical stage that is treated as the quasi steady vortex state. The evo
lution of such states is mainly determined by the slow deformation of the
semiclassical localization curve. The report is based on the paper [5].\n\
nThis is joint work with A.V. Shapovalov.\n\n[1] V.P. Maslov\, The Complex
WKB Method for Nonlinear Equations (I. Linear Theory. Birkhauser Verlag\,
Basel\, 1994).\n\n[2] V.V. Belov\, S.Y. Dobrokhotov\, Semiclassical Maslo
v asymptotics with complex phases. I. General approach. Theor. Math. Phys.
92(2)\, 843–868 (1992).\n\n[3] V.G. Bagrov\, V.V. Belov\, A.Y. Trifonov
\, Semiclassical trajectory-coherent approximation in quantum mechanics I.
High-order corrections to multidimensional time-dependent equations of Sc
hrödinger type. Ann. Phys. 246(2)\, 231–290 (1996).\n\n[4] V.V. Belov\,
A.Y. Trifonov\, A.V. Shapovalov\, The trajectory-coherent approximation a
nd the system of moments for the Hartree type equation. Int. J. Math. Math
. Sci. 32(6)\, 325–370 (2002).\n\n[5] Kulagin\, A.\, Shapovalov\, A. Sem
iclassical states localized on a one-dimensional manifold and governed by
the nonlocal NLSE with an anti-Hermitian term. Eur. Phys. J. Plus 141\, 14
(2026). https://doi.org/10.1140/epjp/s13360-025-07236-6\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. A. Gordin (National Research University "Higher School of Econo
mics"\, Hydrometeorological Research Center of the Russian Federation\, Mo
scow Institute of Physics and Technology\, Innopolis University)
DTSTART:20260402T110000Z
DTEND:20260402T120000Z
DTSTAMP:20260404T111326Z
UID:mmandim/109
DESCRIPTION:Title: The compact finite-difference scheme and modified Richardson extr
apolation for NLSE\nby V. A. Gordin (National Research University "Hig
her School of Economics"\, Hydrometeorological Research Center of the Russ
ian Federation\, Moscow Institute of Physics and Technology\, Innopolis Un
iversity) as part of Mathematical models and integration methods\n\n\nAbst
ract\nA compact finite-difference scheme combined with predictor-corrector
approach for solving quasilinear partial differential equations and syste
ms is presented. The nonlinear Schrödinger equation (NLSE) serves as a mo
del problem to demonstrate the method’s capabilities. The proposed algor
ithm achieves fourth-order spatial accuracy and second-order temporal accu
racy while maintaining computational efficiency through linearization via
Newton — Raphson iterations. As a rule\, one iteration is sufficient. Th
e scheme was optimized according to the Courant parameter based on the cri
terion: the ratio of computational complexity to solution accuracy.\n\nAls
o\, we introduce a modified two-dimensional and quasi-two-dimensional Rich
ardson extrapolation technique that further enhances accuracy up to eighth
-order.\n\nNumerical experiments confirm the scheme’s high precision and
stability across a range of Courant parameters as well as a good conserva
tion of many first integrals of NLSE. The method is applicable to arbitrar
y smooth initial data and various boundary conditions. We tested its prope
rties on various solutions (solitons\, collision of several solitons\, cha
ins\, short-wave noise). In the latter two cases\, there is an alternation
of chaotic and ordered types of solution behavior.\n\nThis is joint work
with D. P. Milutin.\n
LOCATION:https://stable.researchseminars.org/talk/mmandim/109/
END:VEVENT
END:VCALENDAR