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

Farah M. Al-Askar, Wael W. Mohammed, Mohammad Alshammari and M. El-Morshedy
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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
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

Mathematics, 2022, vol. 10, issue 7, 1-11

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.

Keywords: fractional Zakharov system; stochastic Zakharov system; Riccati–Bernoulli sub-ODE method; Jacobi elliptic function method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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