Abstract
The relaxation of solitions on lattice vibrations in the easy axis Heisenberg model was investigated. It was shown that the soliton dynamics is governed by the nonlinear Schrödinger equation with damping and fluctuation force. The presence of these terms is the consequence of the emission and absorption of real phonons when soliton velocity is greater then the speed of sound in the crystal.As the result of these perturbations there arises the time dependence of soliton parameters.Soliton amplitude decreases followed by the simultaneous increase of the soliton width while its propagation has the diffusion character since the soliton behaves like the classical Brownian particle.
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