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

Autor: Ratbay Myrzakulov, Galya Mamyrbekova, Gulgassyl Nugmanova, Muthusamy Lakshmanan
Jazyk: angličtina
Rok vydání: 2015
Předmět:
Zdroj: Symmetry, Vol 7, Iss 3, Pp 1352-1375 (2015)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym7031352
Popis: 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 Schrödinger 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 Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs.
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