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 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2021
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.56-65
  • Keywords: Dissipative Kundu-Eckhaus equation, Split-step Fourier scheme, Rogue waves, MODULATION INSTABILITY, NUMERICAL ASPECTS, TRAINS
  • Istanbul Technical University Affiliated: Yes

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.