Abelian Toda solitons revisited

TL;DR

This paper reviews and compares two methods for constructing soliton solutions in abelian Toda systems, highlighting that Hirota's method produces a subset of solutions obtainable via the rational dressing method.

Contribution

It provides a systematic comparison of Hirota's and rational dressing methods, demonstrating the latter's broader solution set for abelian Toda systems.

Findings

Hirota's method solutions are a subset of rational dressing solutions

The rational dressing method yields more general soliton solutions

A detailed comparison clarifies the relationship between the two approaches

Abstract

We present a systematic and detailed review of the application of the method of Hirota and the rational dressing method to abelian Toda systems associated with the untwisted loop groups of complex general linear groups. Emphasizing the rational dressing method, we compare the soliton solutions constructed within these two approaches, and show that the solutions obtained by the Hirota's method are a subset of those obtained by the rational dressing method.