Mathematics

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.