Patrick Gerard, "Meeting an integrable PDE : the Benjamin-Ono equation"

Wednesday 12 Feb 2025, 11:00 → 12:00 Europe/Rome

Ex-ISEF/Building-Main Lecture Hall (GSSI)

Abstract:

 

The Benjamin-Ono equation is a PDE from Fluid Mechanics, introduced in 1967.

For more than fifty years, it has focused many research works from mathematicians and physicists, probably because it combines two features : on the one hand, it is a nonlinear Hamiltonian PDE with a non local term. On the other hand, it admits a special structure which allows it to be considered as an integrable PDE. I will try to explain in which sense  this equation is integrable, and to describe the expected  role played in its long time dynamics by special solutions called  the solitons.