09:00
10:00
11:00
12:00
13:00
14:00
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 (30min)
10:30 - 11:00 (30min)
Pause café
›11:00 (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
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
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 (1h30)
12:00 - 13:30 (1h30)
Déjeuner
›13:30 (30min)
13:30 - 14:00 (30min)
Départ bus à 13h30
Départ bus à 13h30
