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

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