SU(N) affine Toda solitons and breathers from transparent Dirac potentials
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.
Keywords
Cite
@article{arxiv.1611.03208,
title = {SU(N) affine Toda solitons and breathers from transparent Dirac potentials},
author = {Michael Thies},
journal= {arXiv preprint arXiv:1611.03208},
year = {2017}
}
Comments
10 pages, 1 figure; v2: several improvements, matches version accepted for publication by JPhysA