information:filtering
Wave equations

Equations of wave motion are called wave equations. The solutions to a wave equation give the time-evolution and spatial dependence of the amplitude. Boundary conditions determine if the solutions describe traveling waves or standing waves.

From classical equations of motion and field equations; mechanical, gravitational wave, and electromagnetic wave equations can be derived. The general linear wave equation in 3D is:

where X = X (r, t) is any mechanical or electromagnetic field amplitude, say:

and v is the phase velocity. Nonlinear equations model the dependence of phase velocity on amplitude, replacing v by v (X). There are other linear and nonlinear wave equations for very specific applications, see for example the Korteweg–de Vries equation.