Extreme waves emerging in full 2D+1 dimensional environments

Abstract:

Processes that lead to the formation of extreme events are of major interest in many physical contexts, such as water waves, optics, Bose-Einstein condensate, geophysics, etc. In the last years a great effort from the scientific community has been devoted to their understanding. In the specific case of nonlinear and dispersive wave systems (the topic of the present proposal), a number of mechanisms have been discussed in the literature. The simplest one is the superposition mechanism that holds for every linear wave system. From a statistical point of view, such a mechanism is well understood and the probability of appearance of extreme waves can be calculated. However, more recently, in the field of ocean waves and nonlinear optics, it has been established that the presence of nonlinearity on top of dispersion can lead to changes in the tail of the probability density function of the wave amplitude. This result, established for one-dimensional propagation (1D+1), has been associated with the existence of exact solutions, known as breathers, of integrable equations such as the Nonlinear Schrodinger equation. A number of experimental and theoretical papers on the subject have appeared, establishing many interesting properties of these breathers, as for example their recurrence behavior. Despite many details still need to be investigated, the physics of extreme waves in one dimensional propagation is well understood from a theoretical point of view and the results predicted are well reproduced in wave tank and optical fiber experiments.

For many physical systems, the one-dimensional propagation is an approximation of a more complicated dynamics that takes place in two or more dimensions. The existence of extreme waves in these conditions is much less understood from a theoretical point of view and very few experiments have been performed. Our proposal aims at attacking this problem from a deterministic, statistical, and experimental point of view. In the past, collaborations between researchers of different fields have been very fruitful to establish a common background for tackling the one-dimensional problem; in this respect, our team is composed by experts in the field of ocean waves, nonlinear optics and theoretical physics with expertise both on statistical, deterministic and experimental aspects. Specifically, we intend to:

1) apply the instanton theory to characterize statistically extreme waves in 2D+1 dimension;
2) apply the finite-gap theory to study analytically the dynamics of rogue waves in 2D+1 dimension;
3) characterize numerically new classes of wave solutions that describe dispersive and diffractive spatio-temporal localized wave packets in nonlinear quadratic and cubic media; 4) analyze experimentally the dynamics and statistics of rogue waves in 2D+1 optical and ocean waves.