THE KINETIC-EQUATION FOR SOLITONS AND THE PROBLEM OF ENTROPY PRODUCTION FOR A FULL INTEGRABLE SYSTEM

The kinetical equation for the distribution function of solitons is pr esented. Different cases of soliton's scattering processes were consid ered and the collision integrals for this cases were found. Ail scatte ring processes of solitons were divided Into two types. The first one is the scattering processes with the soliton's coordinates changing on ly, the second-the scattering processses with the soliton's impulces c hanging. The collision integral of solitons due to the scattering of t hem by a thermal hath of quasiparticles is found. It is shown the coll ision integral has the form of coordinates derivities like the Fokker- Plank's collision integral with derivites on impulces. It was given a proof of the entropy production theorem for full integrable system. Th e coefficient of diffusion, coefficient of internal friction, coeffici ent of thermal conductivity were calculated. It is shown the each tran sport coefficient is a sum of two terms. First of its due by the first type of collision, and the second one-by the second type.