Evolution of Rogue Waves in Interacting Wave Systems

Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled nonlinear Schrödinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves below θc all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the nonlinear Schrödinger equations, and should be of interest when designing optical wave guides.