In this article, we take into account the $(2+1)$-dimensional stochastic Chiral nonlinear Schrödinger equation (2D-SCNLSE) in the Itô sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solutions, using three vital methods, namely Riccati–Bernoulli sub-ODE, He’s variational and sine–cosine methods. These solutions may be applicable in various applications in applied science. The proposed methods are direct, efficient and powerful. Moreover, we investigate the effect of multiplicative noise on the solution for 2D-SCNLSE by introducing some graphs to illustrate the behavior of the obtained solutions.

In this article, the stochastic Hirota–Maccari system forced in the Itô sense by multiplicative noise is considered. We just use the He’s semi-inverse method, sine–cosine method, and Riccati–Bernoulli sub-ODE method to get new stochastic solutions which are hyperbolic, trigonometric, and rational. The major benefit of these three approaches is that they can be used to solve similar models. Furthermore, we plot 3D surfaces of analytical solutions obtained in this article by using MATLAB to illustrate the effect of multiplicative noise on the exact solution of the Hirota–Maccari method.

Here, we analyze the (2+1)-dimensional stochastic modified Kordeweg–de Vries (SmKdV) equation perturbed by multiplicative white noise in the Stratonovich sense. We apply the mapping method to obtain new trigonometric, elliptic, and rational stochastic fractional solutions. Because of the importance of the KdV equation in characterizing the behavior of waves in shallow water, the obtained solutions are beneficial in interpreting certain fascinating physical phenomena. We plot our figures in MATLAB and show several 3D and 2D graphical representations to show how the multiplicative white noise affects the solutions of the SmKdV. We show that the white noise around zero stabilizes SmKdV solutions.

In this paper, we consider the stochastic Burgers' equation, which is forced by multiplicative noise in the Stratonovich sense. To get a new trigonometric and hyperbolic stochastic solutions, we apply $\exp (-\phi (\mu ))$-expansion method. In addition, we demonstrate the effect of multiplicative noise on the exact solutions of the Burgers' equation by introducing some graphic representations.