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Emergent hydrodynamics of soliton gases in integrable systems: INI-RIMS Collaboration

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Soliton gases represent infinite random ensembles of interacting solitons displaying  nontrivial large-scale  behaviours ultimately determined by the properties of the elementary two-soliton collisions.  The emergent hydrodynamics of non-equilibrium soliton gases in integrable dispersive systems such as the Korteweg-de Vries and nonlinear Schr\”odinger equations is described by the universal 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 spectral  theory of soliton gases and its connection with the fundamental concept of ``integrable turbulence’’ introduced by Zakharov in 2009. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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