Kinetic and transport equations for localized excitations in the sine-Gordon model

We analyze the kinetic behavior of localized excitations--solitons, breathers, and phonons--in the Sine-Gordon model. Collision integrals for all types of localized excitation collision processes are constructed, and the kinetic equations are derived. We prove that the entropy production in the system of localized excitations takes place only in the case of inhomogeneous distribution of these excitations in real and phase space. We derive transport equations for soliton and breather densities, temperatures, and mean velocities, i.e., show that collisions of localized excitations lead to the creation of diffusion, thermoconductivity, and intrinsic friction processes. The diffusion coefficients for solitons and breathers, describing the diffusion processes in real and phase space, are calculated. It is shown that diffusion processes in real space are much faster than the diffusion processes in phase space.