Affine Toda Solitons and Automorphisms of Dynkin Diagrams

TL;DR

This paper constructs soliton solutions for affine Toda field theories using Hirota's method, leveraging automorphisms of Dynkin diagrams to extend results to both twisted and untwisted algebras.

Contribution

It introduces a novel approach to derive solutions for twisted affine Toda theories via automorphisms of Dynkin diagrams.

Findings

Explicit soliton solutions for simply-laced affine algebras.

Extension of solutions to twisted and untwisted algebras.

Method demonstrates the role of Dynkin diagram automorphisms in integrable models.

Abstract

Using Hirota's method, solitons are constructed for affine Toda field theories based on the simply-laced affine algebras. By considering automorphisms of the simply-laced Dynkin diagrams, solutions to the remaining algebras, twisted as well as untwisted, are deduced.