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

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 + 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.

Keywords

• Heisenberg ferromagnet equation
• integrable systems
• solitons
• nonlinear Schrodinger equations
• gauge equivalence
• nonlinear Schrodinger-Maxwell-Bloch equations
• Lax epresentations
• spin systems