A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions

We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra of arbitrary rank. This allows us to explicitly derive its particular solutions by using dressing technique. We discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have analogues in the case of the Heisenberg ferromagnet equation for the same Lie algebra and are new even in that special case.