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

Abstract

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.