Abstract: I will discuss a new type of a derivative nonlinear Schrödinger equation, which can be seen as a continuum version of completely integrable CalogeroMoser manybody systems in classical mechanics. The resulting NLS exhibits many intriguing features such as a Lax pair structure on Hardy spaces, L2criticality, and turbulent solutions. In this talk, I will focus on dynamics of multisoliton solutions, which exhibit an unbounded growth of Sobolev norms (turbulence). This is based on joint work with Patrick Gérard (Orsay).

This lecture was part of the biannual 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