Abstract: I will discuss a new type of a derivative nonlinear Schrödinger equation, which can be seen as a continuum version of completely integrable Calogero-Moser many-body systems in classical mechanics. The resulting NLS exhibits many intriguing features such as a Lax pair structure on Hardy spaces, L2-criticality, and turbulent solutions. In this talk, I will focus on dynamics of multi-soliton 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 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
18 янв 2024
