Growth of Sobolev norms and dynamics of the nonlinear Schrödinger equation on the torus

Emanuele Haus
Univ. Federico II Napoli
Thursday, April 5, 2018 - 14:30

I will present some recent results concerning the dynamics of semilinear Schrödinger equations on the n-dimensional torus. On the one hand, I will talk about some results exhibiting the existence of solutions that display an unstable behavior and undergo a large growth of Sobolev norms. On the other hand, I will show a result concerning the existence of some special time-quasiperiodic solutions with nonlinear beatings. These two types of solutions have a common feature: despite having small amplitude, they have a genuinely nonlinear behavior, deviating significantly from the dynamics of the free Schrödinger equation on the torus.

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