Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field

TL;DR

This study investigates rogue wave phenomena in chaotic wave fields generated by the Kundu-Eckhaus equation, revealing how nonlinear terms and parameters influence rogue wave probability and wave dynamics.

Contribution

It introduces analysis of rogue wave occurrence in the Kundu-Eckhaus equation, highlighting the effects of nonlinear terms and parameters on wave behavior and rogue wave probability.

Findings

Rogue wave probability depends on the propagation constant k.

The probability is significantly affected by quintic and Raman-effect nonlinear terms.

Wave filament velocity aligns with the average group velocity from dispersion relations.

Abstract

In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution however direction of propagation is controlled by the $\beta$ parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrodinger equation have also been presented.