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


Our goal is to compute excited states for the nonlinear Schr"odinger 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.

Christophe Besse
Christophe Besse
Senior researcher

My research interests are applied mathematics, scientific computing and numerical analysis.