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On the dynamics of a continuum spin system

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

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.

Suggested Citation

  • Lakshmanan, M. & Ruijgrok, Th.W. & Thompson, C.J., 1976. "On the dynamics of a continuum spin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 577-590.
    • Handle: RePEc:eee:phsmap:v:84:y:1976:i:3:p:577-590
    DOI: 10.1016/0378-4371(76)90106-0
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    Cited by:

    1. Rahul, O.R. & Murugesh, S., 2019. "Rogue breather modes: Topological sectors, and the ‘belt-trick’, in a one-dimensional ferromagnetic spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 262-269.

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