Evolution of rogue waves in interacting wave systems

¹  Department of Mathematics, Uppsala University - SE-751 06 Uppsala, Sweden, EU
²  Umeå Plant Science Center, Department of Forest Genetics and Plant Physiology, Swedish University of Agricultural Sciences - SE-901 83 Umeå, Sweden, EU
³  Department of Physics, Umeå University - SE-901 87 Umeå, Sweden, EU

Corresponding author: gronlund@math.uu.se

Received: 4 December 2008
Accepted: 16 March 2009

Abstract

Large-amplitude water waves on deep water have long been known in the seafaring community, and are 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 non-linear Schrödinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle of the direction of the interacting waves, below which 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 non-linear Schrödinger equations, and should be of interest when designing optical wave guides.