BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thibault Congy DTSTART:20200429T150000Z DTEND:20200429T160000Z DTSTAMP:20260404T170630Z UID:WOW/6 DESCRIPTION:Title: Bidirectional soliton gas\nby Thibault Congy as part of Waves in On e World (WOW) series\n\n\nAbstract\nThe soliton structure plays a fundamen tal role in many physical systems due to its fundamental feature: its shap e remains unchanged after the collision with another soliton in the case o f integrable dynamics. Such particle-like behaviour has been at the origin of a new mathematical object: the soliton gas\, consisting of an incohere nt collection of solitons for which phases (positions) and spectral parame ters (e.g. amplitudes) are randomly distributed. The study of soliton gase s involves the description of the gas dynamics as well as the correspondin g modulation of the nonlinear wave field statistics\, which makes the soli ton gas a particularly interesting embodiment of the particle-wave duality of solitons.\n\nMotivated by the recent realisation of bidirectional soli ton gases in a shallow water experiment\, we investigate two integrable mo dels of bidirectional wave: the nonlinear Schrödinger equation and the Ka up-Boussinesq equation. Using a physical approach\, we derive the so-calle d kinetic equation that governs the gas dynamics for the two integrable sy stems. We notably show that the structure of the kinetic equation depends on the "isotropic" or the "anisotropic" nature of the solitons interaction . Additionally we derive expressions for statistical moments of the physi cal fields (e.g. mean water level). As an illustration of the theory\, we solve numerically the gas shock tube problem describing the collision of t wo "cold" soliton gases. An excellent agreement with exact solutions of t he kinetic equations is observed.\n LOCATION:https://stable.researchseminars.org/talk/WOW/6/ END:VEVENT END:VCALENDAR