Computation of excited states for nonlinear Schrödinger equations

par M. Romain Duboscq (Institut de Mathématiques de Toulouse)

mardi 30 avr. 2024, 11:15 → 12:15 Europe/Paris

Amphi Schwartz (IMT)

In this talk, I’ll discuss the computation of excited states for some nonlinear Schrödinger equations. Typically, these states can be understood as critical points of the energy associated to the equation when the mass is fixed. Another point of view is to consider them as critical points of the action associated to the equation when they belong in a Nehari manifold. Here, we focus on radial nodal excited states (states that are radial and have both a positive and negative part). Our approach is based on the observation that we can define « nodal Nehari manifolds » in the radial setting where we’ll search for our excited states. This insight then paves the way to a numerical method, called the Nehari method, that enables us to compute numerically excited states. This is a joint work with INSMI’s famous director and Stefan Le Coz.