Connected and disconnected stable regions of solitons of nonlinear Schr\"odinger equation with $\mathcal{PT}$-symmetric potential

TL;DR

This paper investigates the stability and existence of bright and dark solitons in a nonlinear Schrödinger equation with a $ ext{PT}$-symmetric potential, providing exact solutions, stability analysis, and numerical validation.

Contribution

It presents new exact stationary solutions for solitons in a $ ext{PT}$-symmetric potential and analyzes their stability regions through linear stability analysis and simulations.

Findings

Identified connected and disconnected stable regions of solitons.

Demonstrated stability differences in $ ext{PT}$-broken and unbroken phases.

Validated stability results with numerical simulations.

Abstract

We have considered cubic nonlinear Schr\"odinger equation along with supersymmetric $\mathcal{PT}$ like potential and obtained exact stationary solutions in terms of bright and brigh-dark interacting solitons. The $\mathcal{PT}$ broken and $\mathcal{PT}$ unbroken regions are demonstrated also depicted. Connected and disconnected stable regions of bright and dark solitons are examined incorporating linear stability analysis validated by direct numerical simulations. Moreover, the strength of stability has been illustrated through excitations of bright and dark solitons.