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)

Yannick Bonthonneau ----------------------- Inverse analytic scattering

Let M be Riemannian manifold with boundary. For z=(x,v) an incoming vector on the boundary, we denote by S(x,v) the tangent vector to the geodesic starting from z, at its next point of intersection with the boundary. If M is supposed analytic, under geometric and dynamical assumptions, the geodesic scattering map S determines M, even without prior knowledge of its topology.

12:15 - 13:30 (1h15)

Déjeuner

13:30 - 17:00 (3h30)

Visite du laboratoire souterrain de Modane

19:30 - 21:00 (1h30)

Dîner

Programme