The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation

In the current study, we investigate stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered term is multiplicative noise in Itô sense. By combining F-expansion approach two separate equations, such as Riccati and elliptic new hyperbolic, trigonometric, rational, Jacobi solutions for SBBME-BD can be generated. to are useful understanding various scientific phenomena, including Rossby waves spinning fluids drift plasma. Our results presented using MATLAB, numerous 3D 2D figures illustrating impacts of white on obtained SBBME-BD.