Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2025

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

Résumé

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.

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Dates et versions

hal-04151806 , version 1 (05-07-2023)
hal-04151806 , version 2 (05-11-2024)

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Christophe Besse, Romain Duboscq, Stefan Le Coz. Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis. ESAIM: Mathematical Modelling and Numerical Analysis, 2025, 59 (2), pp.899 - 923. ⟨10.1051/m2an/2025009⟩. ⟨hal-04151806v2⟩
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