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

Hydrodynamic reductions: N ≥ 3.Theorem (El, Kamchatnov, Pavlov & Zykov 2008)N-component hydrodynamic type system∂ t u i = ∂ x (u i v i ), i = 1, . . .,N ,v i = ξ i +N∑ǫ ik u k (v k − v i ), ǫ ik = ǫ ki ,k=1where ξ 1 , ξ 2 , . . . , ξ N are constants and ǫ is a constant symmetric matrix,ǫ ik = ǫ ki , is:diagonalizablelinearly degenerate,semi-Hamiltonian (i.e. integrable - Tsarev 1985, 1991),for any N.The proof is based on the theory of integrable linearly degeneratehydrodynamic type systems developed by Pavlov (1987) and Ferapontov(1991).Gennady ElKinetic equation for a soliton gas