English

Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials

Exactly Solvable and Integrable Systems 2015-08-18 v2

Abstract

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schr\"odinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax pairs.

Keywords

Cite

@article{arxiv.1305.0098,
  title  = {Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials},
  author = {R. Myrzakulov and G. Mamyrbekova and G. Nugmanova and M. Lakshmanan},
  journal= {arXiv preprint arXiv:1305.0098},
  year   = {2015}
}

Comments

21 pages

R2 v1 2026-06-22T00:09:24.965Z