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Solitary Wave Solutions of a Hyperelastic Dispersive Equation

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  • Yuheng Jiang

    (Key Laboratory of Mathematics and Information Networks, Beijing University of Posts and Telecommunications, Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Yu Tian

    (Key Laboratory of Mathematics and Information Networks, Beijing University of Posts and Telecommunications, Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Yao Qi

    (Key Laboratory of Mathematics and Information Networks, Beijing University of Posts and Telecommunications, Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

Abstract

This paper explores solitary wave solutions arising in the deformations of a hyperelastic compressible plate. Explicit traveling wave solution expressions with various parameters for the hyperelastic compressible plate are obtained and visualized. To analyze the perturbed equation, we employ geometric singular perturbation theory, Melnikov methods, and invariant manifold theory. The solitary wave solutions of the hyperelastic compressible plate do not persist under small perturbations for wave speed c > − β k 2 . Further exploration of nonlinear models that accurately depict the persistence of solitary wave solution on the significant physical processes under the K-S perturbation is recommended.

Suggested Citation

  • Yuheng Jiang & Yu Tian & Yao Qi, 2024. "Solitary Wave Solutions of a Hyperelastic Dispersive Equation," Mathematics, MDPI, vol. 12(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:564-:d:1338394
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    References listed on IDEAS

    as
    1. Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
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