| Contents |
| We will discuss some recent progress in the mathematically rigorous study of out-of-equilibrium behavior of nonlinear dispersive equations. The main focus will be on the phenomena of energy cascade as measured in terms of the growth of Sobolev norms of solutions. We study this cascade phenomenon for the cubic nonlinear Schrodinger equation and report on some first rigorous results in this direction of research (joint work with Benoit Pausader, Nikolay Tzvetkov, and Nicola Visciglia). |
|