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 the Whitham <strong>equation</strong>s to kinetic <strong>equation</strong> <strong>for</strong><strong>soliton</strong>sAssuming the existence of the invariant spectral measurecharacterising spatially homogeneous <strong>soliton</strong> <strong>gas</strong>, we want todescribe slow evolution of this measure <strong>for</strong> an inhomogeneous<strong>gas</strong>, i.e. to derive kinetic <strong>equation</strong> <strong>for</strong> <strong>soliton</strong>s.Similarity with the <strong>for</strong>mulation of the Whitham modulation theory(but with the averaging over ensemble rather than period!).P.D. Lax (1991): The zero dispersion limit, a deterministic analogueof turbulence.Hence our interest in the thermodynamic limit of the Whitham<strong>equation</strong>s.Gennady El<strong>Kinetic</strong> <strong>equation</strong> <strong>for</strong> a <strong>soliton</strong> <strong>gas</strong>
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