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

07/05/2023

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by   Christophe Besse, et al.

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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.