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, cilt.11, sa.1, ss.56-65, 2021 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 11 Konu: 1
  • Basım Tarihi: 2021
  • Dergi Adı: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Sayfa Sayıları: ss.56-65

Özet

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.