Generalized Lattice Heisenberg Magnet Model and Its Quasideterminant Soliton Solutions

Abstract

We consider a Darboux transformation of a generalized lattice (or semidiscrete) Heisenberg magnet (GLHM) model. We define a Darboux transformation on solutions of the Lax pair and on solutions of the spin evolution equation of the GLHM model. The solutions are expressed in terms of quasideterminants. We give a general expression for K-soliton solutions in terms of quasideterminants. Finally, we obtain one- and two-soliton solutions of the GLHM model using quasideterminant properties.