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

摘要

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