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:20260423T035617Z UID:WOW/6 DESCRIPTION:Title: Bidi rectional soliton gas\nby Thibault Congy as part of Waves in One World (WOW) series\n\n\nAbstract\nThe soliton structure plays a fundamental rol e in many physical systems due to its fundamental feature: its shape remai ns unchanged after the collision with another soliton in the case of integ rable dynamics. Such particle-like behaviour has been at the origin of a n ew mathematical object: the soliton gas\, consisting of an incoherent coll ection of solitons for which phases (positions) and spectral parameters (e .g. amplitudes) are randomly distributed. The study of soliton gases invol ves the description of the gas dynamics as well as the corresponding modul ation of the nonlinear wave field statistics\, which makes the soliton gas a particularly interesting embodiment of the particle-wave duality of sol itons.\n\nMotivated by the recent realisation of bidirectional soliton gas es in a shallow water experiment\, we investigate two integrable models of bidirectional wave: the nonlinear Schrödinger equation and the Kaup-Bous sinesq equation. Using a physical approach\, we derive the so-called kinet ic equation that governs the gas dynamics for the two integrable systems. We notably show that the structure of the kinetic equation depends on the "isotropic" or the "anisotropic" nature of the solitons interaction. Addi tionally we derive expressions for statistical moments of the physical fie lds (e.g. mean water level). As an illustration of the theory\, we solve n umerically the gas shock tube problem describing the collision of two "col d" soliton gases. An excellent agreement with exact solutions of the kine tic equations is observed.\n LOCATION:https://researchseminars.org/talk/WOW/6/ END:VEVENT END:VCALENDAR