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

被引：9

作者：

Al-Askar, Farah M. ^{[1
]}

Mohammed, Wael W. ^{[2
,3
]}

Alshammari, Mohammad ^{[2
]}

El-Morshedy, M. ^{[4
,5
]}

机构：

[1] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

[2] Univ Hail, Fac Sci, Dept Math, Hail 2440, Saudi Arabia

[3] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

[4] Prince Sattam Bin Abdulaziz Univ, Coll Sci & Humanities Al Kharj, Dept Math, Al Kharj 11942, Saudi Arabia

[5] Mansoura Univ, Fac Sci, Dept Stat & Comp Sci, Mansoura 35516, Egypt

来源：

MATHEMATICS | 2022年 / 10卷 / 07期

关键词：

fractional Zakharov system; stochastic Zakharov system; Riccati-Bernoulli sub-ODE method; Jacobi elliptic function method; DIFFUSION; EQUATION;

D O I：

10.3390/math10071194

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：11

共 28 条

[1]

[Anonymous], 2012, Numerical solution of SDE through computer experiments

[2]

Arnold L., 2003, Random Dynamical Systems

[3] From continuous time random walks to the fractional Fokker-Planck equation [J].