Stability of matter-wave solitons in a density-dependent gauge theory

TL;DR

This paper analyzes the linear stability of chiral matter-wave solitons in a density-dependent gauge theory, showing they are stable similarly to standard Bose-Einstein condensate solitons through analytical and numerical methods.

Contribution

It demonstrates that the stability of these solitons can be effectively studied using the Gross-Pitaevskii framework and the Vakhitov-Kolokolov criterion, providing new insights into their robustness.

Findings

Solitons are stable to linear perturbations.

Stability reduces to the standard Gross-Pitaevskii equation.

Numerical simulations confirm absence of instabilities.

Abstract

We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed.