Evolution of Rogue Waves in Interacting Wave Systems

TL;DR

This paper investigates how rogue waves evolve in systems of two interacting waves modeled by coupled nonlinear Schrödinger equations, revealing different scaling behaviors depending on the interaction angle.

Contribution

It introduces a new analysis of rogue wave formation in interacting wave systems, identifying a critical angle that separates distinct dynamical regimes.

Findings

Different scaling behaviors above and below the critical angle theta_c

Wave systems below theta_c behave similarly to non-interacting waves

Results applicable to optical wave guide design

Abstract

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 Schroedinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle theta_c of the direction of the interacting waves below theta_c 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 Schroedinger equations, and should be of interest when designing optical wave guides.