On a Solitonic Specialisation for the General Solutions of Some Two-Dimensional Completely Integrable Systems

TL;DR

This paper develops a method to construct soliton solutions for a broad class of two-dimensional integrable systems, extending previous work to include non-abelian affine Toda theories using a group-algebraic approach.

Contribution

It introduces a solitonic specialization technique for general solutions of integrable systems, including non-abelian cases, expanding the scope of solution methods in the field.

Findings

Constructed explicit soliton solutions for non-abelian affine Toda theories.

Extended the solitonic specialization approach to a wider class of integrable systems.

Demonstrated the applicability of the group-algebraic framework for solution construction.

Abstract

Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely integrable systems arising in the framework of the group-algebraic approach, including the \lq\lq non-abelian" version of the affine Toda theory.