On reflectionless nature of self-consistent multi-soliton solutions in Bogoliubov-de Gennes and chiral Gross-Neveu models

TL;DR

This paper proves that self-consistent multi-soliton solutions in Bogoliubov-de Gennes and chiral Gross-Neveu models are reflectionless and provides conditions for systems with only right-movers, enhancing understanding of soliton properties.

Contribution

The authors directly prove from the gap equation that these solutions must be reflectionless and extend the self-consistent conditions to systems with only right-movers.

Findings

Self-consistent multi-soliton solutions are reflectionless.

Derived self-consistent conditions for systems with only right-movers.

Extended previous work with complementary results.

Abstract

Recently the most general static self-consistent multi-soliton solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems are derived by the present authors [D. A. Takahashi and M. Nitta, Phys. Rev. Lett. 110, 131601 (2013)]. Here we show a few complementary results, which were absent in the previous our work. We prove directly from the gap equation that the self-consistent solutions need to have reflectionless potentials. We also give the self-consistent condition for the system consisting of only right-movers, which is more used in high-energy physics.