On the dynamics of a continuum spin system

Abstract

For a one-dimensional system of classical spins with nearest neighbour Heisenberg interaction we derive the equation of motion for each three-dimensional spin vector. In the continuum limit where the spins lie dense on a line this set of equations reduces to a nonlinear partial differential equation. In addition to spin-wave solutions we obtain some other special solutions of this equation. In particular we find solitary waves having total energy localised in a finite region, with velocity of propagation inversely proportional to the width of this region. Solutions of still another type are shown to have a diffusive character. The stability of such solutions and the possibility of interaction of two or more solitary waves have not yet been studied.