IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1338-d1092818.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1338/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/6/1338/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    3. Wael W. Mohammed & Mohammed Alshammari & Clemente Cesarano & Sultan Albadrani & M. El-Morshedy, 2022. "Brownian Motion Effects on the Stabilization of Stochastic Solutions to Fractional Diffusion Equations with Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-9, April.
    4. Tahira Sumbal Shaikh & Muhammad Zafarullah Baber & Nauman Ahmed & Naveed Shahid & Ali Akgül & Manuel De la Sen, 2023. "On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    5. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Mahmoud El-Morshedy, 2023. "Solitary Wave Solution of a Generalized Fractional–Stochastic Nonlinear Wave Equation for a Liquid with Gas Bubbles," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    6. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2023. "On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations," Mathematics, MDPI, vol. 11(16), pages 1-17, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1338-:d:1092818. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.