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Solitary Waves Of The Fractal Regularized Long-Wave Equation Traveling Along An Unsmooth Boundary

Author

Listed:
  • KANG-JIA WANG

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • GENG LI

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • JING-HUA LIU

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • GUO-DONG WANG

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

Abstract

The unsmooth boundary has a great influence on the solitary wave form of a nonlinear wave equation. It this work, we for the first time ever propose the fractal regularized long-wave equation which can describe the shallow water waves under the unsmooth boundary (such as the fractal seabed). The fractal variational principle is established and is proved to have a strong minimum condition by the He–Weierstrass theorem. Then, the solitary wave solution is obtained by the fractal variational method which can reduce the order of differential equation and obtain the optimal solution by the stationary condition. Finally, the impact of the unsmooth boundary on the solitary wave is presented. It shows that the fractal order can affect the wave morphology, but cannot affect its peak value. The finding in this paper is important for the coast protection and expected to bring a light to the study of the fractal theoretical basis in the geosciences.

Suggested Citation

  • Kang-Jia Wang & Geng Li & Jing-Hua Liu & Guo-Dong Wang, 2022. "Solitary Waves Of The Fractal Regularized Long-Wave Equation Traveling Along An Unsmooth Boundary," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-6, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500086
    DOI: 10.1142/S0218348X22500086
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    Cited by:

    1. Khater, Mostafa M.A., 2023. "Computational simulations of propagation of a tsunami wave across the ocean," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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