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

C. Senthil Kumar·M. Lakshmanan·B. Grammaticos·A. Ramani
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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.

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C. Senthil Kumar, M. Lakshmanan, B. Grammaticos, A. Ramani. 2006-04-10. Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis. https://doi.org/10.1016/j.physleta.2006.03.074

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