Group theory of a nonlinear spin field model in 2 + 1 dimensions

G. Profilo, G. Soliani and L. Solombrino

Physica A: Statistical Mechanics and its Applications, 1993, vol. 192, issue 1, 175-196

Abstract: We have studied both the compact and the noncompact version of an integrable nonlinear spin field system in 2 + 1 dimensions, the so-called Ishimori model, within a group theory framework. This model possesses an infinite-dimensional symmetry algebra with a loop algebra structure. Using the one-dimensional subalgebras of the symmetry algebra of the model under investigation, we find reduced equations which yield new classes of solutions of the original system from the known ones. The reduced equations obtained are of three types, i.e. the isotropic Heisenberg magnet model, the Landau-Lifshitz magnet model with uniaxial anisotropy, and a system in two independent variables resembling the static Ishimori equations. Our symmetry approach shows the physical meaning of the Ishimori model as being a well-defined phenomenological integrable nonlinear spin field model in 2 + 1 dimensions.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:192:y:1993:i:1:p:175-196

DOI: 10.1016/0378-4371(93)90151-S

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