Journées EDP 2024 - Sciencesconf.org

9:00 - 10:30 (1h30)

Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type

In this mini-course, I will study two integrable nonlinear dispersive equations on the line : the Benjamin-Ono equation and the more recently introduced Calogero-Moser derivative nonlinear Schrödinger equation. The following topics will be discussed. 1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae. 2. Conservation laws and global wellposedness. 3. Traveling waves and multi-solitons. 4. Zero-dispersion limit.

10:30 - 11:00 (30min)

Pause café

11:00 - 12:00 (1h)

Yvan Martel -------------------- Asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation with an internal mode.

I will present a result concerning the asymptotic stability of small solitary waves for the one-dimensional Schrödinger equation with a cubic-quintic, focusing-focusing nonlinearity. For this model, the linearized operator around a small solitary wave has an internal mode whose contribution to the dynamics is handled by checking a nonlinear condition related to the Fermi golden rule. Reference: Yvan Martel, Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation, arXiv:2312.11016

12:00 - 13:30 (1h30)

Déjeuner

13:30 - 14:00 (30min)

Départ bus à 13h30

Programme