Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlev\'e analysis
Exactly Solvable and Integrable Systems
2009-11-11 v1
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-Painlev\'e type and is expected to be nonintegrable.
Keywords
Cite
@article{arxiv.nlin/0604017,
title = {Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlev\'e analysis},
author = {C. Senthil Kumar and M. Lakshmanan and B. Grammaticos and A. Ramani},
journal= {arXiv preprint arXiv:nlin/0604017},
year = {2009}
}
Comments
11 pages. to be published in Phys. Lett. A (2006)