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Keywords = nonlinear Schrodinger-Maxwell-Bloch equations

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24 pages, 234 KiB  
Article
Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials
by Ratbay Myrzakulov, Galya Mamyrbekova, Gulgassyl Nugmanova and Muthusamy Lakshmanan
Symmetry 2015, 7(3), 1352-1375; https://doi.org/10.3390/sym7031352 - 3 Aug 2015
Cited by 61 | Viewed by 5941
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 Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry Breaking)
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