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Solitary Wave Solutions for the Higher Dimensional Jimo-Miwa Dynamical Equation via New Mathematical Techniques

Author

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  • Aly R. Seadawy

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

  • Hanadi Zahed

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

  • Mujahid Iqbal

    (Faculty of Science, Jiangsu University, Zhenjiang 212013, China)

Abstract

In this study, under the considerations of symbolic computation with the help of Mathematica software, various types of solitary wave solutions for the (3 + 1)-dimensional Jimo–Miwa (JM) equation are successfully constructed based on the extended modified rational expansion method. The constructed solutions are novel and more general for the JM equation named kink wave solutions, anti-kink wave solutions, bright and dark solutions, mixed solutions in the shape of bright-dark solutions, and periodic waves, which do not exist in the existing literature. The physical phenomena of the demonstrated results is represented graphically by two-dimensional, three-dimensional, and contour images with the help of Mathematica. The obtained results will be widely used to explain the various interesting physical structures in the areas of optics, plasma, gas, acoustics, classical mechanics, fluid dynamics, heat transfer, and many others.

Suggested Citation

  • Aly R. Seadawy & Hanadi Zahed & Mujahid Iqbal, 2022. "Solitary Wave Solutions for the Higher Dimensional Jimo-Miwa Dynamical Equation via New Mathematical Techniques," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1011-:d:776571
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    References listed on IDEAS

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    1. Chen, Yong & Yan, Zhenya, 2005. "New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 399-406.
    2. Seadawy, Aly R. & Cheemaa, Nadia, 2019. "Propagation of nonlinear complex waves for the coupled nonlinear Schrödinger Equations in two core optical fibers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 529(C).
    3. Yun-Mei Zhao, 2013. "F -Expansion Method and Its Application for Finding New Exact Solutions to the Kudryashov-Sinelshchikov Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, April.
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    Cited by:

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