Generic transverse stability of kink structures in atomic and optical nonlinear media with competing attractive and repulsive interactions

TL;DR

This paper shows that topological kink structures in atomic and optical media with mixed attractive and repulsive interactions are stable and robust, offering new ways to control topological excitations in experiments.

Contribution

It demonstrates the generic stability of kink structures across various models with competing interactions, supported by analytical and numerical analysis.

Findings

Kink structures are stable despite transverse instabilities.

Stability is confirmed through linearization and direct simulations.

Results are applicable to cold atom and optical experiments.

Abstract

We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and three-dimensional extended Gross-Pitaevskii models with quantum fluctuations describing droplet-bearing environments but also to the two-dimensional cubic-quintic nonlinear Schr\"odinger equation containing higher-order corrections to the nonlinear refractive index. Contrary to the generic dark soliton transverse instability, the kink structures are generically robust under the interplay of low-amplitude attractive and high-amplitude repulsive interactions. A quasi-1D effective potential picture dictates the existence of these defects, while their stability is obtained numerically and analytically through linearization analysis and direct dynamics in the presence of external fluctuations showcasing their unprecedented resilience. These generic (across different models) findings should be detectable in current cold atom and optics experiments, offering insights towards controlling topological excitations.