Dr Maksim Pavlov, Instytut Lebiediewa, Moskwa

Integrability of new nonlocal kinetic equation

We study a new class of nonlinear kinetic equations recently derived in the context of the description of nonequilibrium dynamics of dense soliton gases with elastic collisions. These kinetic equations have nonlocal structure and can be obtained by considering the infinite-genus thermodynamic limit for the Whitham modulation systems for soliton equations. We prove that the N-component `cold-gas' hydrodynamic reductions of the nonlocalkinetic equation represent integrable linearly degenerate hydrodynamic type systems. Explicit formulae for the Riemann invariants and characteristic velocities are obtained for N=3. For this case, a family of exact similarity solutions is obtained and existence of quasi-periodic three-phase solutions is proved. An explicit representation for the family of linearly degenerate hydrodynamic symmetries is found.