Computation of excited states for the nonlinear Schr{\"o}dinger equation: numerical and theoretical analysis

TL;DR

This paper introduces a new numerical technique based on the Nehari manifold for computing excited states of the nonlinear Schrödinger equation, comparing it with the classical shooting method in terms of accuracy and speed.

Contribution

The paper presents a novel Nehari manifold approach for excited state computation and compares its performance with the classical shooting method.

Findings

Nehari method accurately computes excited states on large domains.

Nehari method is slower than the shooting method.

Comparison highlights trade-offs between accuracy and computational speed.

Abstract

Our goal is to compute excited states for the nonlinear Schr{\"o}dinger equation in the radial setting. We introduce a new technique based on the Nehari manifold approach and give a comparison with the classical shooting method. We observe that the Nehari method allows to accurately compute excited states on large domains but is relatively slow compared to the shooting method.