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

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

2006-04-10

arxiv.org/abs/nlin/0604017v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1016/j.physleta.2006.03.074

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-Painlev\'e type and is expected to be nonintegrable.

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