Abstract
Resonance phenomena can lead to large-amplitude fluctuations that can no longer be analyzed perturbatively, yet play a fundamental role either because of their impact (extreme events) or because they profoundly alter the nature of the physical model (tipping points). This is the case, for example, with rogue waves.
The mathematical study of these highly nonlinear waves can be conducted either deterministically using sophisticated PDE techniques (solitons, front propagation, classification of singularities, etc.) or statistically by quantifying the probability of large deviations from Gaussian noise and by describing the dynamic precursors of these rare events.
