The Korteweg–de Vries Equation, often abbreviated as KdV, 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 equation is significant in various fields, including fluid dynamics and mathematical physics. Developed in the 19th century by Diederik Korteweg and G. de Vries, the KdV equation has applications beyond water waves, such as in plasma physics and traffic flow. Its solutions can exhibit solitons, which are stable, localized wave packets that maintain their shape while traveling at constant speeds.