Kinetic Equations and Integrable Hamiltonian Systems
A survey of interrelations between kinetic equations and integrable systems is presented. We discuss common origin of special classes of solutions of the Boltzmann kinetic equation for Maxwellian particles and special solutions for integrable evolution equations. The thermodynamic limit and soliton kinetic equation for the integrable Korteweg-de Vries equation are considered. The existence of decaying and degenerate dispersion laws and the appearance of additional integrals of motion for the interacting waves is discussed.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 6, pp 869-882.
Citation Example: Belokolos E. D. Kinetic Equations and Integrable Hamiltonian Systems // Ukr. Mat. Zh. - 2005. - 57, № 6. - pp. 731–741.