Gap solitons of a super-Tonks-Girardeau gas in a one-dimensional periodic potential

TL;DR

This paper investigates the stability and formation of gap solitons in a super-Tonks-Girardeau gas within a one-dimensional periodic potential, revealing conditions for stability and relationships with nonlinear Bloch waves.

Contribution

It provides a detailed stability analysis and numerical verification of gap solitons and their relation to nonlinear Bloch waves in the super-Tonks-Girardeau phase, highlighting new formation conditions.

Findings

Increasing potential amplitude stabilizes gap solitons.

Higher-family gap solitons form near the bottom of band gaps.

Gap solitons are related to nonlinear Bloch waves.

Abstract

We study the stability of gap solitons of the super-Tonks-Girardeau bosonic gas in one-dimensional periodic potential. The linear stability analysis indicates that increasing the amplitude of periodic potential or decreasing the nonlinear interactions, the unstable gap solitons can become stable. In particular, the theoretical analysis and numerical calculations show that, comparing to the lower-family of gap solitons, the higher-family of gap solitons are easy to form near the bottoms of the linear Bloch band gaps. The numerical results also verify that the composition relations between various gap solitons and nonlinear Bloch waves are general and can exist in the super-Tonks-Girardeau phase.