Growth of Sobolev norms for the nonlinear Schrodinger equation near some quasiperiodic tori
Zaher Hani
Georgia Tech USA
Co-Author(s): Marcel Guardia, Emanuele Haus, Alberto Maspero, Michela Procesi
Abstract:
We consider the 2D cubic nonlinear Schrodinger equation. This equation admits a family of quasiperiodic solutions coming from the complete integrability of the 1D model. We prove the existence of solutions to the 2D NLS equation that start very close to those quasiperiodic solutions (in appropriate Sobolev norms) and then become very far away in the same topology.