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.

21 pages

References in corpus (8)

• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Rogue waves of the Hirota and the Maxwell-Bloch equations
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis
• On the integrable inhomogeneous Myrzakulov I equation
• Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions
• Integrable Heisenberg Ferromagnet Equations with self-consistent potentials
• Integrable inhomogeneous Lakshmanan-Myrzakulov equation

Cited by in corpus (17)

• Integrable Kuralay equations: geometry, solutions and generalizations
• Darboux Transformation and Exact Solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
• Darboux transformations and exact soliton solutions of integrable coupled spin systems related with the Manakov system
• Integrable Motion of Curves, Spin Equation and Camassa-Holm Equation
• Fifth-order generalized Heisenberg supermagnetic models
• Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation
• Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation
• Darboux tranformation and solutions of the (2+1)-dimensional Schrödinger-Maxwell-Bloch equation
• Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence
• Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions
• The (2+1)-dimensional Hirota-Maxwell-Bloch equation: Darboux transformation and soliton solutions
• Soliton Equations with Self-Consistent Sources
• Dispersionless Limits of Some Integrable Equations
• Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations
• Darboux Transformation and Exact Solutions of the Myrzakulov-Lakshmanan-II Equation
• Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence