Unveiling dynamic solitons in the (2+1)-dimensional Kadomtsev–Petviashvili equation: Insights from fluids and plasma

In this study, we examine soliton solutions of extended (2+1)-dimensional Kadomtsev–Petviashvili equation arising in fluid mechanics and plasma physics. The research utilizes an improved modified extended tanh-function method to derive new soliton solutions. The diverse set of soliton solutions obtained in this study, featuring a combination of rational, trigonometric, and hyperbolic functions, enhances the model’s applicability for real-world fluid mechanics and plasma physics scenarios. The visual representations of the obtained solutions through contour, three-dimensional, and two-dimensional depictions in various simulations are shown in the figures. The results propose that the employed method is an efficient and powerful tool to be implemented for different differential equations in applied sciences and engineering.