Dispersive partial differential equation

Summary

A dispersive partial differential equation is an evolution equation whose plane waves travel at speeds that depend on their frequency. A localized solution, made of many frequencies, therefore spreads out in space and decays in amplitude while its energy is conserved. The main examples are the Schrödinger equation, the Korteweg–De Vries equation and the Klein–Gordon equation. Dispersion competes with nonlinear effects, and the balance between the two produces phenomena such as solitons.