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We investigate the rogue wave dynamics of the dissipative Kundu-Eckhausequation. With this motivation, we propose a split-step Fourier scheme for itsnumerical solution. After testing the accuracy and stability of the schemeusing an analytical solution as a benchmark problem, we analyze the chaoticwave fields generated by the modulation instability within the frame of thedissipative Kundu-Eckhaus equation. We discuss the effects of variousparameters on rogue wave formation probability and we also discuss the role ofdissipation on occurrences of such waves.

A Split-Step Fourier Scheme for the Dissipative Kundu-Eckhaus Equation and its Rogue Wave Dynamics