Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...

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From the Whitham equations to kinetic equation forsolitonsAssuming the existence of the invariant spectral measurecharacterising spatially homogeneous soliton gas, we want todescribe slow evolution of this measure for an inhomogeneousgas, i.e. to derive kinetic equation for solitons.Similarity with the formulation 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 Whithamequations.Gennady ElKinetic equation for a soliton gas
OutlineKinetic equation for solitons as the thermodynamic limit ofthe Whitham equationsGeneralised kinetic equationHydrodynamic reductions and integrabilityConclusionsAlso, if time permits;Moments of the wave fieldFurther research directionsGennady ElKinetic equation for a soliton gas
Page 1 and 2: Kinetic equation for a soliton gasG
Page 3: From N-solitons/N-gap potentials to
Page 7 and 8: The Whitham equationsThe differenti
Page 9 and 10: Thermodynamic limitThe total densit
Page 11 and 12: Kinetic equation for solitons: smal
Page 13 and 14: Hydrodynamic reductions of the kine
Page 15 and 16: Hydrodynamic reductions: N ≥ 3.Th
Page 17 and 18: Linearly degenerate conservation la
Page 19 and 20: N=3: explicit formulae (El, Kamchat
Page 21 and 22: References[1] El, G.A., Krylov A.L.
Page 23 and 24: Wave field moments in a soliton gas
Page 25 and 26: Appendix 1. N=3: Exact solutions.1.
Page 27 and 28: Appendix 2. Kinetic equation for th
Page 29: A2. Kinetic equation for the focusi

Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...

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