Solving non-abelian loop Toda equations

TL;DR

This paper develops a method to construct soliton solutions for non-abelian loop Toda equations related to general linear groups, focusing on the untwisted case using rational dressing techniques.

Contribution

It introduces a rational dressing method tailored for non-abelian loop Toda equations with a specific block-matrix representation.

Findings

Successfully constructs soliton solutions for the equations.

Provides a systematic approach for the untwisted case.

Enhances understanding of non-abelian integrable systems.

Abstract

We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation suggested by the initial $\bbZ$-gradation.