Quasideterminant solutions of the generalized Heisenberg magnet model

TL;DR

This paper develops Darboux transformations for the generalized Heisenberg magnet model using quasideterminants, constructing multi-soliton solutions and relating them to dressing method results, with explicit solutions for SU(2).

Contribution

It introduces quasideterminant-based Darboux transformations for the GHM model and connects these solutions with the dressing method, providing explicit solutions for SU(2).

Findings

Constructed multi-soliton solutions via quasideterminants.

Linked Darboux transformation solutions with dressing method results.

Derived explicit soliton solutions for SU(2) case.

Abstract

In this paper we present Darboux transformation for the generalized Heisenberg magnet (GHM) model based on general linear Lie group GL(n) and construct multi-soliton solutions in terms of quasideterminants. Further we relate the quasideterminant multi-soliton solutions obtained by the means of Darboux transformation with those of obtained by dressing method. We also discuss the model based on the Lie group SU(n) and obtain explicit soliton solutions of the model based on SU(2).