On the reflection of solitons of the nonlinear Schrodinger equation

TL;DR

This paper numerically investigates how solitons of the 2D nonlinear Schrödinger equation reflect off solid walls, demonstrating perfect reflection on vertical walls and imperfect reflection on diagonal walls using a Crank-Nicolson finite element scheme.

Contribution

It introduces a numerical study of soliton reflection phenomena with detailed simulations of different wall orientations using an implicit-explicit finite element method.

Findings

Perfect reflection of solitons on vertical walls

Imperfect reflection of dark solitons on diagonal walls

Validation of the numerical scheme for soliton-wall interactions

Abstract

In this paper we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D nonlinear Schrodinger equation as the underlying mathematical model and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.