ASYMPTOTIC STABILITY OF MULTI-SOLITONS FOR 1D SUPERCRITICAL NLS

Series
PDE Seminar
Time
Tuesday, September 30, 2025 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Abdon Moutinho – Georgia Tech – aneto8@gatech.eduhttps://sites.google.com/view/abdon-moutinho-neto/
Organizer
Gong Chen

Motivated by the Soliton Resolution Conjecture, the study of dynamics of multi-solitons has been crucial to understand the  long-time behavior of solutions for dispersive PDEs.

In this talk, we consider one-dimensional L2 supercritical nonlinear Schrödinger equation.

It is well-known that the solitons for this model are unstable, but conditional asymptotic stability for a single soliton was obtained in the pioneering work of Krieger and Schlag. In this talk, using the linear and scattering theory developed in our previous work, we show the conditional strong asymptotic stability for any multi-solitons with large separation in the speed. More precisely,  this solution of the supercritical NLS will converge asymptotically in the H1 norm to a finite of multi-solitons moving with constant speeds plus a radiation (Scattering of the remainder).  Finally, at the end of the talk, we discuss our ongoing research related to this topic.  This is a joint work with Gong Chen.