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

More documents

Recommendations

Info

The Whitham equations (KdV case)The generating equation for the KdV-Whitham system is (Flaschka,Forest, McLaughlin 1979)(dp N ) t = (dq N ) x ,where dp N and dq N are the quasimomentum and quasienergydifferentials on the hyperelliptic Riemann surface of genus N:R 2 (λ) =∏(λ − λ j ), λ ∈ C, λ j ∈ R .2N+1j=1Asymptotic behaviour near λ = −∞:−λ ≫ 1 : dp N ∼ − dλ(−λ) 1/2 ,dq N ∼ (−λ) 1/2 dλGennady ElKinetic equation for a soliton gas
The Whitham equationsThe differentials dp N and dq N are uniquely defined by the normalisation:∮dp N (λ) = 0 ,β i∮dq N (λ) = 0 ,β ii = 1, . . .,N . j 1 2 j3 42 N 1gapband2 j 1The fundamental wavenumbers k j and frequencies ω j are found as∮∮k j (λ 1 , . . .,λ 2N+1 ) = dp N (λ), ω j (λ 1 , . . . , λ 2N+1 ) = dq N (λ),α j 2 jα jGennady 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: OutlineKinetic equation for soliton
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 ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?