Abstract: I will show how the Lax pair structure of the Benjamin-Ono equation on the line leads to an explicit formula for general initial data in the Sobolev space H1. Applications to the zero-dispersion limit will be discussed.

Patrick Gérard is a French mathematician interested in partial differential equations, in particular microlocal analysis, control theory and nonlinear dispersive equations in connection with the notion of weak turbulence.

This lecture was part of the bi-annual Abel Symposium.

This year the title of the symposium was Partial Differential Equations waves, Nonlinearities and Nonlocalities.

The symposium was funded by
- The Norwegian Academy of Sciences and Letters via the Abel board and The Norwegian Mathematical Society
- NTNU Norwegian University of Science and Technology
- Research Council of Norway via the grant Waves and Nonlinear Phenomena
- Trond Mohn Foundation