Modulation equations approach for solving vortex and radiation in nonlinear Schrodinger equation

TL;DR

This paper develops a modulation equations approach to analyze vortex and radiation solutions in the 2D nonlinear Schrödinger equation, providing a new algorithm for vortex detection and numerical simulations of scattering.

Contribution

It derives full modulation equations for vortex and radiation dynamics and introduces an efficient algorithm for vortex identification with numerical solutions.

Findings

Successful numerical simulations of vortex and radiation scattering

Effective algorithm for vortex detection with varying energy and spin

Accurate numerical solutions of the modulation equations

Abstract

We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schr\"{o}dinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are derived. A general algorithm is proposed to efficiently and accurately find vortices with different values of energy and spin index. The modulation equations are solved by accurate numerical method. Numerical tests and simulations of scattering are given.