ON ANALYTICAL SOLUTIONOF KDV EԚUATION BY LAPLACE TRANSFORMS METHOD

ADVISOR: BOKA KUMSA BOLE (PhD, Associate Professor) Most of nonlinear partial differential equations have many applications in this real world. The Korteweg-De Vries (KdV) equation is a fundamental nonlinear partial differential equation that arises in various physical phenomena, including shallow water waves, plasma physics, and nonlinear optics. Furthermore, to find the solutions of nonlinear partial differential equations are not simply soluble and henceforth different modified methods were practiced to get solutions of such equations. Due to its nonlinear nature, finding exact solutions to the KdV equation is often challenging. From different types of methods of solving of KdV equation, in this study, we consider the Laplace Transform Method and its application. So this study presents an analytical solution of the KdV equation using the Laplace transform method. The process provides an effective analytical approach to deal with initial-boundary value problems for nonlinear partial differential equations. Detailed derivations, step-by-step methodology, and illustrative examples are included to ensure comprehensive understanding.<br> Keywords: Analytical, KdV equation, Laplace transform method and inverse of Laplace transform method.