The Korteweg-de Vries equation (KdV equation) is a mathematical model that describes the propagation of shallow water waves. It is a third-order partial differential equation that captures the balance between nonlinearity and dispersion in wave motion. The KdV equation is significant in various fields, including fluid dynamics and soliton theory. One of the key features of the KdV equation is its ability to produce solitons, which are stable, localized wave packets that maintain their shape while traveling at constant speeds. This property makes the KdV equation important for understanding wave phenomena in different physical systems, such as ocean waves and plasma physics.