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 Schr\"odinger 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 Schr\"odinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax pairs.

/pdf/integrable-2-1-dimensional-spin-models-with-self-consistent-2z6qifbzn4.pdf

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

Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

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 Schrodinger 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 Schrodinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrodinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs.

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

Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.

Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials

Darboux Transformation and Exact Solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials

We study the connection between some lattice and continuous Heisenberg spin models. The continuous limits of some generalized compressible Heisenberg spin chains are found. Using the methods of differential geometry of surfaces, the Lakshmanan equivalent counterpart of one of the obtained continuous Heisenberg ferromagnet equation is constructed.

On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains

A new class of two-dimensional surfaces generated by formulas which are generalizations of the well known Lelieuvre and Schief formulas is presented. These surfaces are connected with two-dimensional spin systems which are stationary versions of the (2+1)-dimensional classical continuous Heisenberg ferromagnets.

N. S. Serikbaev

Papers

On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains

On the Geometry of Stationary Heisenberg Ferromagnets