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The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative

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  • Wael W. Mohammed

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Farah M. Al-Askar

    (Department of Mathematical Science, Collage of Science, Princess Nourah Bint, Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Elkhateeb S. Aly

    (Mathematics Department, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia)

Abstract

The stochastic shallow water wave equation (SSWWE) in the sense of the beta-derivative is considered in this study. The solutions of the SSWWE are obtained using the F-expansion technique with the Riccati equation and He’s semi-inverse method. Since the shallow water equation has many uses in ocean engineering, including river irrigation flows, tidal waves, tsunami prediction, and weather simulations, the solutions discovered can be utilized to represent a wide variety of exciting physical events. We create many 2D and 3D graphs to demonstrate how the beta-derivative and Brownian motion affect the analytical solutions of the SSWWE.

Suggested Citation

  • Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Elkhateeb S. Aly, 2023. "The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1338-:d:1092818
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    References listed on IDEAS

    as
    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2022. "The Analytical Solutions of the Stochastic mKdV Equation via the Mapping Method," Mathematics, MDPI, vol. 10(22), pages 1-9, November.
    2. Farah M. Al-Askar & Wael W. Mohammed & Qura tul Ain, 2022. "The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, August.
    3. Farah M. Al-Askar & Wael W. Mohammed & Abeer M. Albalahi & Mahmoud El-Morshedy, 2022. "The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method," Mathematics, MDPI, vol. 10(5), pages 1-9, March.
    4. Wael W. Mohammed & A. M. Albalahi & S. Albadrani & E. S. Aly & R Sidaoui & A. E. Matouk & A. M. Nagy, 2022. "The Analytical Solutions of the Stochastic Fractional Kuramoto–Sivashinsky Equation by Using the Riccati Equation Method," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-8, May.
    Full references (including those not matched with items on IDEAS)

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