The KdV Equation and Solitons

Application ID: 85

The Korteweg-de Vries (KdV) equation models water waves. It contrasts sharply to the Burgers equation, because it introduces no dissipation and the waves travel seemingly forever. Solitons have their primary practical application in optical fibers. Specifically, a fiber’s linear dispersion properties level out a wave while the nonlinear properties give a focusing effect. The result is a very stable, long-lived pulse. This solution says that the pulse’s speed determines its amplitude and width. This simulation illustrates this effect.

This model example illustrates applications of this type that would nominally be built using the following products: