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


Bayındır C. , Yurtbak H.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.11, no.1, pp.56-65, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2021
  • Title of Journal : TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Page Numbers: pp.56-65

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.