Finding The Solution of The Korteweg–De Vries Equation Using The Gelfand–Levitan–Marchenko Method

This article presents the solution of the inverse scattering problem for the Korteweg–de Vries (KdV) equation using the Gelfand–Levitan–Marchenko (GLM) integral equation. The study considers the determination of scattering data based on initial conditions and the method for reconstructing a unique potential function from these data. The main idea of the GLM method, its mathematical foundations, and its application to the KdV equation are presented in a systematic manner.