Solitons and quasi-Grammians of the generalized lattice Heisenberg magnet model

Abstract

In this paper, we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model. We calculate the quasi-Grammian solutions by the iteration of standard binary Darboux transformation. Furthermore, we derive the explicit matrix solutions for the binary Darboux matrix and then reduce them to the elementary Darboux matrix and plot the dynamics of solutions.