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Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Author

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  • Chaudry Masood Khalique

    (International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
    Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli Str., 71, Baku AZ1007, Azerbaijan
    These authors contributed equally to this work.)

  • Karabo Plaatjie

    (International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
    These authors contributed equally to this work.)

Abstract

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

Suggested Citation

  • Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1439-:d:578557
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    References listed on IDEAS

    as
    1. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    2. Du, Xia-Xia & Tian, Bo & Qu, Qi-Xing & Yuan, Yu-Qiang & Zhao, Xue-Hui, 2020. "Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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