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Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model

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  • Tariq, Kalim U.
  • Wazwaz, Abdul-Majid
  • Javed, Rizwan

Abstract

In this study, the coupled nonlinear (1＋1)-dimensional Drinfel’d–Sokolov–Wilson (DSW) equation in dispersive water waves is investigated. The proposed structure is very important nonlinear evolution model in mathematical physics and engineering, which is used to describe nonlinear surface gravity wave propagating over horizontal sea bed. By using three analytical approaches namely, the new extended hyperbolic function method, the modified extended tan hyperbolic function method and the new (G′G2)-expansion method, some new traveling wave solutions for the suggested nonlinear model are derived. As a result, a variety of multi soliton solutions structures in the form of dark, multi-bell shaped, singular bell shaped, trigonometric, hyperbolic and rational functions are obtained via proposed methods. By choosing appropriate set of parameters, the 3D, contour and 2D plots for some solutions are also demonstrated to visualize their nature in an efficient way. The modulation instability and stability analysis for the observed solutions are also addressed. The results obtained demonstrate the effectiveness, conciseness, and efficiency of the applied integration techniques, which may be applied to investigate more complex models arising in contemporary science and engineering.

Suggested Citation

  • Tariq, Kalim U. & Wazwaz, Abdul-Majid & Javed, Rizwan, 2023. "Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010827
    DOI: 10.1016/j.chaos.2022.112903
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    References listed on IDEAS

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    1. Izadi, Mohammad & Roul, Pradip, 2022. "Spectral semi-discretization algorithm for a class of nonlinear parabolic PDEs with applications," Applied Mathematics and Computation, Elsevier, vol. 429(C).
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    Cited by:

    1. Li, Yan & Hao, Xiazhi & Yao, Ruoxia & Xia, Yarong & Shen, Yali, 2023. "Nonlinear superposition among lump soliton, stripe solitons and other nonlinear localized waves of the (2+1)-dimensional cpKP-BKP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 57-70.
    2. Haitham Qawaqneh & Jalil Manafian & Mohammed Alharthi & Yasser Alrashedi, 2024. "Stability Analysis, Modulation Instability, and Beta-Time Fractional Exact Soliton Solutions to the Van der Waals Equation," Mathematics, MDPI, vol. 12(14), pages 1-23, July.
    3. Haitham Qawaqneh & Khalil Hadi Hakami & Ali Altalbe & Mustafa Bayram, 2024. "The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model," Mathematics, MDPI, vol. 12(17), pages 1-17, September.

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