Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation

TL;DR

This paper develops quasideterminant solutions for a non-Abelian Toda lattice using Darboux transformations and applies these to study kink interactions in a matrix sine-Gordon equation.

Contribution

It introduces quasideterminant solutions for a generalized non-Abelian Toda lattice and explores kink interactions in a reduced matrix sine-Gordon model.

Findings

Quasideterminant solutions effectively describe the non-Abelian Toda lattice.

Kink solutions exhibit specific interaction properties.

The approach provides a new method for solving matrix integrable systems.

Abstract

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of polarized kink solutions.