On the gauge equivalence of the Landau-Lifshitz and the nonlinear Schrödinger equations on symmetric spaces

Abstract

The gauge equivalence between a generalized Heisenberg spin chain (G/H) in the classical and continuum limit and the nonlinear Schrödinger equation (NLSE), with special attention to noncompact groups, is established. It has been demonstrated that noncompact groups allow a richer spectrum of possible reductions of the Heisenberg system to the NLSE. Some specialities of the model with nontrivial boundary conditions are discussed. The gauge equivalence between single-axis anisotropic Landau-Lifshitz equations (LLE) and isotropic LLE is briefly discussed.