### Selection of standing waves at small energy for NLS with a trapping potential in 1 D

- Series
- PDE Seminar
- Time
- Tuesday, September 5, 2023 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Online: https://gatech.zoom.us/j/95574359880?pwd=cGpCa3J1MFRkY0RUeU1xVFJRV0x3dz09
- Speaker
- Scipio Cuccagna – Universita` di Trieste – scuccagna@units.it

Due to linear superposition, solutions of a Linear Schrodinger Equation with a trapping potential, produce a discrete quasiperiodic part. When a nonlinear perturbation is turned on, it is known in principle, and proved in various situations, that at small energies there is a phenomenon of standing wave selection where, up to radiation, quasiperiodicity breaks down and there is convergence to a periodic wave. We will discuss this phenomenon in 1 D, where cubic nonlinearities are long range perturbations of the linear equations. Our aim is to show that a very effective framework to see these phenomena is provided by a combination of the dispersion theory of Kowalczyk, Martel and Munoz along with Maeda's notion of Refined Profile.