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

## TL;DR

This paper introduces a split-step Fourier numerical scheme for the dissipative Kundu-Eckhaus equation and explores how dissipation influences rogue wave formation and dynamics.

## Contribution

It presents a new numerical method for solving the dissipative Kundu-Eckhaus equation and analyzes rogue wave behavior under different parameters and dissipation effects.

## Key findings

- The scheme is accurate and stable based on benchmark tests.
- Dissipation affects the probability and characteristics of rogue waves.
- Parameter variations influence rogue wave formation and chaos.

## 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.