Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories II

TL;DR

This paper constructs new single soliton solutions in affine Toda field theories, revealing novel topological charges and advancing understanding of the representation weights using inverse scattering methods.

Contribution

It introduces new soliton solutions with unique topological charges in affine Toda theories using a group doublecross product inverse scattering approach.

Findings

New soliton solutions with unobserved topological charges

Progress in filling the weights of fundamental representations

Application of inverse scattering method to rank one solutions

Abstract

New single soliton solutions to the affine Toda field theories are constructed, exhibiting previously unobserved topological charges. This goes some of the way in filling the weights of the fundamental representations, but nevertheless holes in the representations remain. We use the group doublecross product form of the inverse scattering method, and restrict ourselves to the rank one solutions.