On the dynamics of a continuum spin system

M. Lakshmanan, Th.W. Ruijgrok and C.J. Thompson

Physica A: Statistical Mechanics and its Applications, 1976, vol. 84, issue 3, 577-590

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.

Date: 1976
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:84:y:1976:i:3:p:577-590

DOI: 10.1016/0378-4371(76)90106-0

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