Solitary Wave Solutions in (2+1) Dimensions: The KdV Equation Derived from Ideal Fluid Models

In this research article, we study the (2+1)-dimensional Korteweg-de Vries equation (KdV), which is derived from Euler’s equations related to ideal fluid systems. Our primary goal is to obtain explicit solutions utilizing novel methodologies, particularly the new auxiliary equation and the simplest equation methods. We concentrate on the search for solitary wave solutions inside the (2+1)-dimensional KdV, which is relevant in domains such as fluid dynamics, plasma physics and nonlinear waves. Our objective is to increase knowledge of this equation and give insight into the behavior of solitary waves by employing a novel mathematical technique. The bifurcation analysis is also presented for the model problem. This will be accomplished by displaying our findings in 2D and 3D graphics.