Exploring the exact solutions of the Kuramoto-Sivashinsky equation with advection noise in fluid dynamics

In this study, we consider the stochastic Kuramoto-Sivashinsky (SKS) equation driven by advection noise. We show that its exact solution can be obtained by first solving a corresponding deterministic form of the Kuramoto-Sivashinsky equation (DKS) and then combining the results with the solution of a stochastic ordinary differential equation. By Using [Formula: see text]-expansion method, we acquire the exact solutions for the DKS equation. In the absence of noise, we extend some earlier results. Additionally, MATLAB software is employed to generate several 3D plots that illustrate and analyze the influence of advection noise on the solutions of the SKS equation.