On the Breathers of $a_n^{(1)}$ Affine Toda Field Theory

TL;DR

This paper explicitly constructs breather solutions in $a_n^{(1)}$ affine Toda field theory, revealing their topological charge properties and mass relations, thus advancing understanding of their soliton interactions.

Contribution

It provides explicit constructions of breather solutions in $a_n^{(1)}$ affine Toda field theory, detailing their topological charges and mass relations, which was not previously established.

Findings

Breathers can originate from same-species solitons or anti-species solitons.

Breathers from same-species solitons carry topological charges.

Breather masses are less than the sum of constituent soliton masses.

Abstract

Explicit constructions of $a_n^{(1)}$ affine Toda field theory breather solutions are presented. Breathers arise either from two solitons of the same species or from solitons which are anti-species of each other. In the first case, breathers carry topological charges. These topological charges lie in the tensor product representation of the fundamental representations associated with the topological charges of the constituent solitons. In the second case, breathers have zero topological charge. The breather masses are, as expected, less than the sum of the masses of the constituent solitons.