Multicomponent Nonlinear Evolution Equations of the Heisenberg Ferromagnet Type. Local versus Nonlocal Reductions

TL;DR

This paper explores a matrix nonlinear evolution system extending the Heisenberg ferromagnet equation, analyzing local and nonlocal reductions, and introduces a local integrable deformation with various reductions.

Contribution

It introduces a new class of multicomponent nonlinear evolution equations related to Hermitian symmetric spaces, extending the classical Heisenberg ferromagnet model with local and nonlocal reductions.

Findings

Identification of local and nonlocal reductions of the system

Development of a local integrable deformation

Analysis of the extended system's properties

Abstract

The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system under consideration extends the $1+1$ dimensional Heisenberg ferromagnet equation in the sense that its Lax pair has a form rather similar to the pair of the original Heisenberg ferromagnet model. We shall present here certain local and nonlocal reductions. A local integrable deformation and some of its reductions will be discussed too.