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.

10 pages, 1 figure; v2: several improvements, matches version accepted for publication by JPhysA

References in corpus (6)

• Generating AdS String Solutions
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Exact solution of N baryon problem in the Gross-Neveu model
• Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
• Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin