Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis

Abstract

While many integrable spin systems are known to exist in (1+1) and (2+1) dimensions, the integrability property of the physically important (2+1) dimensional isotropic Heisenberg ferromagnetic spin system in the continuum limit has not been investigated in the literature. In this paper, we show through a careful singularity structure analysis of the underlying nonlinear evolution equation that the system admits logarithmic type singular manifolds and so is of non-Painlevé type and is expected to be nonintegrable.

arXiv comment11 pages. to be published in Phys. Lett. A (2006)

References in corpus (3)

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• On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
• A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures

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