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

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ConclusionsThe thermodynamic limit of the Whitham equations associated withhyperelliptic Riemann surfaces leads to the kinetic equations for thecorresponding soliton gases.The original Zakharov (1971) prescription for the determination ofthe velocity of a trial soliton in a rarefied soliton can be directlyextended to the case of the soliton gas of finite density.N-component cold gas hydrodynamic reductions of the generalizedkinetic equation for solitons represent linearly degeneratesemi-Hamiltonian (integrable) systems of hydrodynamic type for anyN.Gennady ElKinetic equation for a soliton gas
References[1] El, G.A., Krylov A.L., Molchanov, S.A. and Venakides, S., ”Solitonturbulence as a thermodynamic limit of stochastic soliton lattices”,Advances in Nonlinear Mathematics and Science, PHYSICA D, 152/153,2001, pp 653-664.[2] El, G.A., ”The thermodynamic limit of the Whitham equations”,PHYS LETT A, 311, 2003, pp 374-383.[3] El, G.A. and Kamchatnov, A.M., ”Kinetic equation for a densesoliton gas”, PHYS REV LETT 95, 2005, Art No 204101, 4 pp.[4] El, G.A., Kamchatnov, A.M., Pavlov, M.V., and Zykov, S.A.,”Nonlocal kinetic equation: integrable hydrodynamic reductions,symmetries and exact solutions” nlin. arXive 2008.Gennady ElKinetic equation for a soliton gas
Page 1 and 2: Kinetic equation for a soliton gasG
Page 3 and 4: From N-solitons/N-gap potentials to
Page 5 and 6: OutlineKinetic equation for soliton
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: N=3: explicit formulae (El, Kamchat
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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