Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
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From N-<strong>soliton</strong>s/N-gap potentials to a <strong>soliton</strong> <strong>gas</strong>N-<strong>soliton</strong>s: two approachesIST: reflectionless potentials (N-<strong>soliton</strong> solutions);Finite-gap theory: closing all spectral bands in the N-gap potentialleads to the N-<strong>soliton</strong>.Soliton <strong>gas</strong>: N → ∞; a generalised reflectionless potential (Marchenko)with shift invariant probability measure on it.IST:Gurevich, Zybin et. al. (2000, 2002): stochastic version of theLax-Levermore approach (KdV and defocusing NLS)Kotani (2008): KdV flow on generalized reflectionless potentials(Sato ’s Grassmanian approach)Finite-gap theory: El, Krylov, Molchanov and Venakides (1999):<strong>soliton</strong> <strong>gas</strong> as the thermodynamic limit of finite-gap potentials:N → ∞ , L → ∞ N/L ∼N∑k j = O(1)j=1Gennady El<strong>Kinetic</strong> <strong>equation</strong> <strong>for</strong> a <strong>soliton</strong> <strong>gas</strong>
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