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

Abstract

The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $A.III$. 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.

This manuscript is based upon a talk given at the XXII-nd International Conference on Geometry, Integrability and Quantization