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The Exact Traveling Wave Solutions Of Local Fractional Generalized Hirota–Satsuma Coupled Korteweg–De Vries Equations Arising In Interaction Of Long Waves

Author

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  • ZONG-GUO ZHANG

    (Division of Mathematics and Artificial Intelligence, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China)

  • SU-LING CHEN

    (College of Intelligence and Information Engineering, Shandong University of Traditional Chinese Medicine, Jinan 250355, P. R. China)

  • QUAN-SHENG LIU

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China)

Abstract

Wave–wave interaction occurs in the propagation deformation of nonlinear long waves in shallow-water. In order to further study the propagation mechanism of shallow-water long waves interaction, the exact traveling wave solutions of the local fractional generalized Hirota–Satsuma coupled Korteweg–de Vries (HS-KdV) equations defined by the Cantor sets are obtained. The non-differentiable solutions with fixed fractal dimension and different propagation velocity are discussed. The results indicate that the exact solutions of the local fractional generalized HS-KdV equations characterize the interaction of fractal long waves with different dispersion relations on shallow-water surfaces.

Suggested Citation

  • Zong-Guo Zhang & Su-Ling Chen & Quan-Sheng Liu, 2024. "The Exact Traveling Wave Solutions Of Local Fractional Generalized Hirota–Satsuma Coupled Korteweg–De Vries Equations Arising In Interaction Of Long Waves," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-9.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401205
    DOI: 10.1142/S0218348X23401205
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