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.
Highlights
Integrable and non-integrable spin systems [1] play a very useful role in nonlinear physics and mathematics
One can include more than one scalar potential and make them interact with the spin vector to generate new integrable spin equations
We start from the so-called Myrzakulov–Lakshmanan II equation (ML-II), which has the form
Summary
Integrable and non-integrable spin systems [1] play a very useful role in nonlinear physics and mathematics. The continuum limit of the Heisenberg ferromagnetic spin system and its various generalizations give rise to some of the important integrable spin systems in (1 + 1) dimensions [6,7] They are intimately related to the nonlinear Schrödinger family of equations through geometrical (or Lakshmanan equivalence or L-equivalence) and gauge equivalence concepts and these systems often admit magnetic soliton solutions [1]. We point out that equivalent (2 + 1)-dimensional integrable nonlinear Schrödinger–Maxwell–Bloch-type evolution equations and their Lax pairs can be identified From these equations, several interesting limiting cases of nonlinear evolution equations in (2 + 1) and (1 + 1) dimensions, along with their. We present some basic features of them
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