Thibault Congy (Northumbria University, UK)
Description
Gas dynamics of solitons in integrable systems
Soliton gases represent infinite random ensembles of interacting solitons displaying nontrivial large-scale behaviours governed by the properties of the elementary two-soliton collisions. The dynamics of non-equilibrium soliton gases in integrable dispersive systems such as the Korteweg-de Vries and nonlinear Schrödinger equations is described by a nonlinear integro-differential kinetic equation for the density of states in the spectral (Lax) phase space. In my talk, I will outline the main ideas of the kinetic theory of soliton gases and its application within the context of integrable turbulence for the Korteweg-de Vries equation.