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.