Algebraic solitons in the massive Thirring model

TL;DR

This paper derives exact algebraic soliton solutions in the massive Thirring model, revealing their spectral properties, interactions, and a novel double-soliton configuration with doubled mass.

Contribution

It introduces explicit algebraic soliton solutions, including a new double-soliton configuration, advancing understanding of soliton interactions in the massive Thirring model.

Findings

Single algebraic solitons correspond to embedded eigenvalues with maximal mass.

A new double-soliton solution with double the mass of a single soliton.

Double-soliton describes slow interaction of two identical algebraic solitons.

Abstract

We present exact solutions describing dynamics of two algebraic solitons in the massive Thirring model. Each algebraic soliton corresponds to a simple embedded eigenvalue in the Kaup--Newell spectral problem and attains the maximal mass among the family of solitary waves traveling with the same speed. By coalescence of speeds of the two algebraic solitons, we find a new solution for an algebraic double-soliton which corresponds to a double embedded eigenvalue. We show that the double-soliton attains the double mass of a single soliton and describes a slow interaction of two identical algebraic solitons.