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

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 chaoti...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 11; no. 1; p. 56
Main Authors Bayindir, C, Yurtbak, H
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2021
Elman Hasanoglu
Subjects
Analysis
Differential equations
Exact solutions
Stability analysis
Water waves
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Summary: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.
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ISSN:2146-1147
2146-1147