SU(N) affine Toda solitons and breathers from transparent Dirac potentials

TL;DR

This paper demonstrates how transparent potentials in the Dirac equation can generate a broad class of multi-soliton and multi-breather solutions in su(N) affine Toda field theories, extending known relationships to complex twisted kinks.

Contribution

It introduces a method to derive classical solutions of affine Toda theories from Dirac potentials, generalizing previous real kink results to complex twisted kinks.

Findings

Generated multi-soliton solutions from Dirac potentials.

Extended the relationship to complex twisted kinks.

Provided Lax representation for the solutions.

Abstract

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1+1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-De Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.