Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

Abstract

In this article, the stochastic Davey–Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some previously obtained results. Due to the significance of the Davey–Stewartson equations in plasma physics, nonlinear optics, hydrodynamics and other fields, the discovered solutions are useful in explaining a number of intriguing physical phenomena. By using MATLAB tools to simulate our results and display some of 3D graphs, we show how the multiplicative Brownian motion impacts the analytical solutions of the SDSEs. Finally, we demonstrate the effect of multiplicative Brownian motion on the stability and the symmetry of the achieved solutions of the SDSEs.

Exact solutions of the stochastic Maccari system forced by multiplicative noise

“…where 𝜎 is a intensity of noise, 𝑊(𝑡) is the standard Wiener process and 𝑊 𝑡 = 𝜕𝑊 𝜕𝑡 . Three different techniques including sine-cosine, the Riccati-Bernoulli sub-ODE, and He's semi-inverse will be utilized to attain the exact solutions of SMS (3)(4). The results reported here generalize earlier results, such as the finding in [29,32].…”

“…The generated solutions can be used to illustrate a number of exciting complicated physical phenomena since the stochastic solutions are more accurate. Finally, we presented some graphics using the MATLAB tool to show how multiplicative noise affects the exact solutions of the stochastic SMS (3)(4).…”

“…Here, we examine the effects of noise on the acquired solutions of SMS (3)(4). In order to illustrate how these solutions behave, we have various graphical representations.…”

“…The format of this article is as follows: In Section 2, we utilize a suitable transformation for converting the stochastic SMS (3)(4) to an ODE form. In Section 3, we attain the exact stochastic solutions for SMS (3-4) using three various methods.…”

“…Finding exact solutions to NLEEs has emerged as one of the most fascinating and fruitful study areas. Numerous efficient techniques for acquiring exact solutions of NLEEs have been displayed, including $$ (G^{\prime }/G)$$‐expansion [1, 2], mapping method [3, 4], tanh‐sech [5, 6], perturbation [7, 8], $$exp(-\Phi (\eta ))$$‐expansion [9], functional variable [10], sine‐cosine [11–13], sech p function [14], Hirota's [15], Jacobi elliptic function [16], Exp‐function [17, 18], Riccati‐Bernoulli sub‐ODE [19], etc.…”