Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 044, 16 pages      arXiv:1302.0637      https://doi.org/10.3842/SIGMA.2013.044

Two-Dimensional Toda-Heisenberg Lattice

Vadim E. Vekslerchik
Institute for Radiophysics and Electronics of NAS of Ukraine, 12, Proskura Str., Kharkiv, 61085, Ukraine

Received February 06, 2013, in final form June 04, 2013; Published online June 12, 2013

Abstract
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.

Key words: classical Heisenberg model; Toda-like lattices; Hirota direct method; Ablowitz-Ladik hierarchy; soliton.

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