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Investigation of shallow water waves near the coast or in lake environments via the KdV–Calogero–Bogoyavlenskii–Schiff equation

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  • Han, Peng-Fei
  • Zhang, Yi

Abstract

Shallow water waves phenomena in nature attract the attention of scholars and play an important role in fields such as tsunamis, tidal waves, solitary waves, and hydraulic engineering. Hereby, for the shallow water waves phenomena in various natural environments, we study the KdV–Calogero–Bogoyavlenskii–Schiff (KdV–CBS) equation. Based on the binary Bell polynomial theory, a new general bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the KdV–CBS equation are derived, and it is proved that it is completely integrable in Lax pair sense. Various types of mixed solutions are constructed by using a combination of Homoclinic test method and symbolic computations. These findings have important significance for the discipline, offering vital insights into the intricate dynamics of the KdV–CBS equation. We hope that our research results could help the researchers understand the nonlinear complex phenomena of the shallow water waves in oceans, rivers and coastal areas. Furthermore, the present work can be directly applied to other nonlinear equations.

Suggested Citation

  • Han, Peng-Fei & Zhang, Yi, 2024. "Investigation of shallow water waves near the coast or in lake environments via the KdV–Calogero–Bogoyavlenskii–Schiff equation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005605
    DOI: 10.1016/j.chaos.2024.115008
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    References listed on IDEAS

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    1. Zhang, Run-Fa & Li, Ming-Chu & Albishari, Mohammed & Zheng, Fu-Chang & Lan, Zhong-Zhou, 2021. "Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2021. "Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Wen-Xiu Ma, 2024. "A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem," Mathematics, MDPI, vol. 12(6), pages 1-12, March.
    5. Ye, Rusuo & Zhang, Yi, 2023. "A vectorial Darboux transformation for the Fokas–Lenells system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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