A SPLIT-STEP FOURIER SCHEME FOR THE DISSIPATIVE KUNDU-ECKHAUS EQUATION AND ITS ROGUE WAVE DYNAMICS

A SPLIT-STEP FOURIER SCHEME FOR THE DISSIPATIVE KUNDU-ECKHAUS EQUATION AND ITS ROGUE WAVE DYNAMICS

C. Bayındır, H. Yurtbak

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Abstract

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.

Keywords

Dissipative Kundu-Eckhaus equation, Split-step Fourier scheme, Rogue waves.