Kinetic and Transport Equations for Localized Excitations in Sine-Gordon Model

Abstract

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