Non-equilibrium dynamics of nonlinear wave systems: turbulent regime, breakdown and wave condensatión

Abstract

The first part of this thesis will be concerned with the study of the statistical behavior in the long time limit of weakly nonlinear wave systems. The deterministic study of waves gives satisfactory solutions in many cases, however, they are rather restricted to some particulars initial conditions. For instance, the dynamics of circular wave produced by throwing a pebble into a pond (Fig 1.1.a), can be properly described by deterministic methods coming from classical fluid mechanics and wave motion. On the other hand, there are numerous examples where this framework fails to properly describe wave motion phenomena, as in the case of wind generated surface waves (Fig 1.1.b) where the deterministic description becomes unmanageable. However, the existence of a large number of degrees of freedom, namely the excited modes in the system, allows us to provide a statistical description. In the case of small wave amplitudes (i.e. weakly nonlinearities) such a statistical description is given in the frame of the today called wave turbulence theory.