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Effects of the Wiener Process on the Solutions of the Stochastic Fractional Zakharov System

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)

  • Mohammad Alshammari

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

  • M. El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

We consider in this article the stochastic fractional Zakharov system derived by the multiplicative Wiener process in the Stratonovich sense. We utilize two distinct methods, the Riccati–Bernoulli sub-ODE method and Jacobi elliptic function method, to obtain new rational, trigonometric, hyperbolic, and elliptic stochastic solutions. The acquired solutions are helpful in explaining certain fascinating physical phenomena due to the importance of the Zakharov system in the theory of turbulence for plasma waves. In order to show the influence of the multiplicative Wiener process on the exact solutions of the Zakharov system, we employ the MATLAB tools to plot our figures to introduce a number of 2D and 3D graphs. We establish that the multiplicative Wiener process stabilizes the solutions of the Zakharov system around zero.

Suggested Citation

  • Farah M. Al-Askar & Wael W. Mohammed & Mohammad Alshammari & M. El-Morshedy, 2022. "Effects of the Wiener Process on the Solutions of the Stochastic Fractional Zakharov System," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1194-:d:787775
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    References listed on IDEAS

    as
    1. Ming Song & Zhengrong Liu, 2012. "Traveling Wave Solutions for the Generalized Zakharov Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-14, July.
    2. Iqbal, Naveed & Wu, Ranchao & Mohammed, Wael W., 2021. "Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 102-119.
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