# Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials

## TL;DR

This paper investigates the existence, stability, and dynamics of solitons in a nonlocal nonlinear Schrödinger equation with PT-symmetric potentials, identifying conditions for stability and phase transitions.

## Contribution

It introduces localized nonlinear modes in a nonlocal NLS with specific PT-symmetric potentials and analyzes their stability and phase behavior.

## Key findings

- Identified parameter regions for broken and unbroken PT phases.
- Determined stability conditions for solitons.
- Numerically demonstrated stable soliton dynamics.

## Abstract

We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schroedinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.