More non-Abelian loop Toda solitons

TL;DR

This paper introduces new soliton solutions for non-Abelian loop Toda equations using rational dressing, extending Hirota's method to matrix generalizations and revealing novel non-Abelian soliton behaviors.

Contribution

It presents the first explicit matrix solutions for non-Abelian loop Toda equations, generalizing Hirota's soliton solutions to a non-Abelian context.

Findings

New non-Abelian soliton solutions discovered

Solutions expressed as matrix generalizations of Hirota's solutions

Method applicable to complex general linear groups

Abstract

We find new solutions, including soliton-like ones, for a special case of non-Abelian loop Toda equations associated with complex general linear groups. We use the method of rational dressing based on an appropriate block-matrix representation suggested by the Z-gradation under consideration. We present solutions in a form of a direct matrix generalization of the Hirota's soliton solution already well-known for the case of Abelian loop Toda systems.