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The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

Author

Listed:
  • Farah M. Al-Askar

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

  • 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)

  • Abeer M. Albalahi

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

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:817-:d:764023
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    References listed on IDEAS

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    1. Tambue, Antoine & Mukam, Jean Daniel, 2019. "Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 23-40.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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    1. Mukam, Jean Daniel & Tambue, Antoine, 2020. "Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4968-5005.

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