Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis
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.
Authors
- Stefan Le Coz (ORCID: https://orcid.org/0000-0003-0680-0175)
- Romain Duboscq (ORCID: https://orcid.org/0000-0002-3739-3640)
- Christophe Besse
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Toulouse III - Paul Sabatier (FR)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- Institut National des Sciences Appliquées de Toulouse (FR)
- Toulouse Mathematics Institute (FR)
- Institut de Mathématiques de Toulouse (FR)
Publication Details
- Journal
- ESAIM. Mathematical modelling and numerical analysis
- Published
- 2025-02-11
- DOI
- https://doi.org/10.1051/m2an/2025009
- Primary Topic
- Nonlinear Photonic Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Centre International de Mathématiques et Informatique de Toulouse