Work

Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis

Year: 2025

Type: article

Abstract: Our goal is to compute excited states for the nonlinear Schrödinger 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.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025009

Authors: Christophe Besse, Romain Duboscq, Stefan Le Coz

Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Institut National des Sciences Appliquées de Toulouse, Université de Toulouse, Institut de Mathématiques de Toulouse

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: Agence Nationale de la Recherche, Centre International de Mathématiques et Informatique de Toulouse