# Families of stable solitons and excitations in the PT-symmetric nonlinear Schrodinger equations with position-dependent effective masses

## TL;DR

This paper investigates the existence, stability, and dynamics of solitons in PT-symmetric nonlinear Schrödinger equations with position-dependent diffraction, revealing new stable solutions and their behaviors in variable media.

## Contribution

It introduces the study of PT-symmetric nonlinear Schrödinger equations with variable diffraction coefficients, finding stable soliton families and analyzing their properties and interactions.

## Key findings

- Stable families of 1D and 2D solitons identified.
- Analytical solutions for some stable solitons derived.
- Soliton dynamics and collisions studied.

## Abstract

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than PT-symmetric ones, but feature similar properties. Our results may suggest new experiments for PT-symmetric nonlinear waves in nonlinear nonuniform optical media.