  We investigate the rogue wave dynamics of the dissipative Kundu-Eckhaus
equation. With this motivation, we propose a split-step Fourier scheme for its
numerical solution. After testing the accuracy and stability of the scheme
using an analytical solution as a benchmark problem, we analyze the chaotic
wave fields generated by the modulation instability within the frame of the
dissipative Kundu-Eckhaus equation. We discuss the effects of various
parameters on rogue wave formation probability and we also discuss the role of
dissipation on occurrences of such waves.
