Kinetical Properties of Solitons in One-Dimentional Model Magnetic Systems

The problem of kinetic properties of excitations in integrable models belongs to the one of the most nontrivial problems of kinetical physics. At first enormous long relaxation of nonlinear excitation has been found in numerical experiments by Fermi Pasta and Ulam (see for example [1]). In Zabusky and Kruskal numerical experiment [2] has been discovered unexpected behavior of localized nonlinear excitations, namely these excitations interact without changing their forms and velocities. Zabusky and Kruskal gave them the term - solitons. Shortly after the analytical method of solving of nonlinear differential equation with partial derivatives - inverse scattering method-was found on the example of Korteveg -de Vries equation for 1+1 dimension [3]. Another physically reasonable continuous models, covered by inverse scattering method are Nonlinear Schrodinger equation, Sine-Gordon equation and Landau-Lifshits equation ’(see [4,5]).