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Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation

Author

Listed:
  • Weifang Yan

    (School of Mathematics and Statistics Science, Ludong University, Yantai 264001, China)

  • Linlin Wang

    (School of Mathematics and Statistics Science, Ludong University, Yantai 264001, China)

  • Min Zhang

    (School of Science, Hunan Institution of Technology, Hengyang 421002, China)

Abstract

In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the bifurcation method of dynamical systems. Then, the persistence of the kink and antikink wave solutions of the perturbed modified Gardner equation is studied by exploiting the geometric singular perturbation theory and the Melnikov function method. When the perturbation parameter is sufficiently small, we obtain the sufficient conditions to guarantee the existence of kink and antikink wave solutions.

Suggested Citation

  • Weifang Yan & Linlin Wang & Min Zhang, 2024. "Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation," Mathematics, MDPI, vol. 12(6), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:928-:d:1361397
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    References listed on IDEAS

    as
    1. Jhangeer, Adil & Hussain, Amjad & Junaid-U-Rehman, M. & Baleanu, Dumitru & Riaz, Muhammad Bilal, 2021. "Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Tang, Yaning & Xu, Wei & Shen, Jianwei & Gao, Liang, 2008. "Persistence of solitary wave solutions of singularly perturbed Gardner equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 532-538.
    3. Sanjaya K. Mohanty & Apul N. Dev & Soubhagya Kumar Sahoo & Homan Emadifar & Geeta Arora & Kang-Jia Wang, 2023. "Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized G′/G-Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2023, pages 1-12, March.
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