On soliton solutions of the time-discrete generalized lattice Heisenberg magnet model

Abstract

Generalized lattice Heisenberg magnet model is an integrable model exhibiting soliton solutions. The model is physically important for describing the magnon bound states (or soliton excitations) with arbitrary spin, in magnetic materials. In this paper, a time-discrete generalized lattice Heisenberg magnet (GLHM) model is investigated. By writing down the Lax pair representation of the time-discrete GLHM model, we present explicitly the underlying integrable structure like, the Darboux transformation and soliton solutions.