Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons

TL;DR

This paper develops transparent boundary conditions for the nonlocal nonlinear Schrödinger equation to enable reflectionless propagation of PT-symmetric solitons, confirmed through numerical simulations.

Contribution

It introduces the first transparent boundary conditions for the nonlocal nonlinear Schrödinger equation, facilitating reflectionless soliton propagation in numerical models.

Findings

Transparent boundary conditions successfully prevent backscattering.

Numerical simulations confirm reflectionless propagation of PT-symmetric solitons.

The method enhances modeling of nonlocal nonlinear wave phenomena.

Abstract

We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schroedinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.