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Data-driven approach to shallow water equation in ocean engineering: Multi-soliton solutions, chaos, and sensitivity analysis

Author

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  • Kazmi, Syeda Sarwat
  • Jhangeer, Adil
  • Riaz, Muhammad Bilal

Abstract

The objective of this research is to explore the dynamics of the shallow water wave equation in extended (3+1) dimensions. This equation is employed to represent atmospheric and oceanic turbulence from various standpoints. Utilizing a multiple exp-function technique, various solitary wave configurations in the form of 1-wave, 2-wave, and 3-wave are generated successfully. This approach is especially advantageous for extracting multisolitons without the need of bilinear forms. To visually illustrate and demonstrate the solutions, they are represented graphically using 3D, 2D, and density plots. Additionally, a qualitative nature of the dynamical system is conducted using bifurcation. Subsequently, an outward force is implemented to the model to create a disturbance, resulting in a modified planar system. The chaotic phenomenon in the modified system is confirmed through various tools designed for chaos detection. Further study is carried out on the model’s sensitivity under three different initial conditions, confirming that the system remains stable and does not exhibit high sensitivity. A newly introduced bidirectional scatter plot approach is employed to perform a comparative analysis of solution behaviors, effectively highlighting overlapping regions and distinctions within their solution spaces through data points, showcasing its innovative contribution. The results of this study are both intriguing and make a notable impact on the area of soliton specifically, as well as on the broader field of mathematical physics.

Suggested Citation

  • Kazmi, Syeda Sarwat & Jhangeer, Adil & Riaz, Muhammad Bilal, 2026. "Data-driven approach to shallow water equation in ocean engineering: Multi-soliton solutions, chaos, and sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 573-595.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pb:p:573-595
    DOI: 10.1016/j.matcom.2025.10.030
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    References listed on IDEAS

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    1. Mann, Nikita & Rani, Setu & Kumar, Sachin & Kumar, Raj, 2024. "Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 473-490.
    2. Pengbo Wan & Jalil Manafian & Hajar Farhan Ismael & Sizar Abid Mohammed, 2020. "Investigating One‐, Two‐, and Triple‐Wave Solutions via Multiple Exp‐Function Method Arising in Engineering Sciences," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    3. Rafiq, Muhammad Hamza & Raza, Nauman & Jhangeer, Adil, 2023. "Dynamic study of bifurcation, chaotic behavior and multi-soliton profiles for the system of shallow water wave equations with their stability," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. 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).
    5. Kumar, Sachin & Kumar, Amit, 2022. "Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 254-274.
    6. Pengbo Wan & Jalil Manafian & Hajar Farhan Ismael & Sizar Abid Mohammed, 2020. "Investigating One-, Two-, and Triple-Wave Solutions via Multiple Exp-Function Method Arising in Engineering Sciences," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-18, June.
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