Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. II. Special Solutions

This paper is a continuation of our previous work in which we studied a sl (3, ℂ) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the corresponding integrable hierarchy of nonlinear evolution equations. Now, we shall demonstrate how one can construct special solutions over constant back- ground through Zakharov-Shabat's dressing technique. That approach will be illustrated on the example of the generalized Heisenberg ferromagnet equation related to the linear problem for sl (3, ℂ). In doing this, we shall discuss the differences between the Hermitian and pseudo-Hermitian cases.