Speaker: Prof. Gennady El (Loughborough Univ., UK)
Title: Isospectral Kinetic Equation for Soliton Gas
Time: 2008-03-27 (Thu.)  16:30 -17:30
Abstract: We present a new class of nonlinear kinetic equations recently derived in the context of the description of nonequilibrium dynamics of dense soliton gases with elastic collisions. These kinetic equations have nonlocal structure and can be obtained by considering the infinite-genus thermodynamic limit for the Whitham modulation systems for soliton equations. We also propose a simple straightforward derivation of the kinetic equation for a soliton gas using the phase-shift expressions for pairwise soliton collisions. We prove that N component ‘cold-gas’ hydrodynamic reductions of the isospectral kinetic equation represent integrable linearly degenerate hydrodynamic type systems for arbitrary N and construct a number of exact solutions for N=3.
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