Emergent hydrodynamics of soliton gases in nonlinear dispersive waves

Abstract: Soliton gases represent large random ensembles of interacting solitons that display non-trivial emergent, macroscopic, behaviours ultimately determined by the properties of the elementary two-soliton collisions. Originally introduced by V. Zakharov in 1971 the concept of soliton gas has recently attracted significant interest from both mathematics and physics communities. The large-scale evolution of non-equilibrium dense soliton gases in integrable dispersive systems 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 spectral theory of soliton gases and its applications to a range of fundamental dispersive hydrodynamic phenomena: from modulational instability to dispersive shock waves.

mathematical physicsanalysis of PDEsclassical analysis and ODEscomplex variablesdynamical systemsfunctional analysisnumerical analysisspectral theory

Audience: researchers in the topic

Nonlinear Waves and Coherent Structures Webinar Series

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