$A_n^{(1)}$ Toda solitons and the dressing symmetry

TL;DR

This paper provides a new elementary derivation of soliton solutions in $A_n^{(1)}$ Toda models, offering explicit expressions and linking to vertex operator formalism, thus broadening the understanding of integrable soliton solutions.

Contribution

It introduces an alternative to the Hirota method for deriving Toda solitons and connects the solutions to the vertex operator formalism, generalizing previous approaches.

Findings

Explicit N-soliton solutions derived without Hirota method

Connection established between solitons and vertex operator formalism

Generalization of sine-Gordon soliton approach

Abstract

We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of monosolitons we suggest a relation to the vertex operator formalism, previously used by Olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed by Babelon and Bernard.