Solitons in $\mathcal{PT}$-symmetric systems with spin-orbit coupling and critical nonlinearity

TL;DR

This paper constructs and analyzes stable one-dimensional solitons in a $ ext{PT}$-symmetric system with spin-orbit coupling and critical quintic nonlinearity, revealing stability regions, evolution scenarios, and interaction behaviors.

Contribution

It introduces the first stable 1D solitons in $ ext{PT}$-symmetric systems with SOC and critical nonlinearity, including stability analysis and interaction dynamics.

Findings

Stable solitons exist in main and annex gaps.

Unstable solitons either blow up, decay, or form breathers.

SOC regularizes solitons beyond the $ ext{PT}$ symmetry-breaking point.

Abstract

We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light propagation in a dual-core waveguide with skewed coupling between the cores. Stability regions for the solitons are identified in the system's parameter space. They include the main semi-infinite gap, and an additional finite $\textit{annex gap}$. Stability boundaries are identified by means of simulations of the perturbed evolution, which agree with results produced by the linear-stability analysis for small perturbations. Distinct evolution scenarios are identified for unstable solitons. Generally, they suffer blowup or decay, while weakly unstable solitons transform into breathers. Due to a regularizing effect of SOC, stationary solitons are also found beyond the exceptional point, at which the $\mathcal{PT}$ symmetry breaks down, but they are unstable. Interactions between adjacent solitons are explored too, featuring rebound or merger followed by blowup. Slowly moving (tilted) solitons develop weak oscillations, while fast ones are completely unstable. Also considered is the reduced diffractionless system, which creates only unstable solitons.