Double peak rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Abstract

We study the properties of the chaotic wave fields generated in the frame of the Sasa- Satsuma equation when a plane wave solution is randomly perturbed with a white noise. We have found that plane waves with different propagation constant splits into selffocused filaments, that propagate with a velocity which is well approximately given by the group velocity calculated from the dispersion relation for the plane wave solution. Different propagation constants are considered and a good agreement is obtained with the numerical solution. We have also calculated the density of probability of having a wave of given amplitude, therefore determining the probability of appearance of rogue waves. Their spectra are also analized.