Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in physics—such as sound waves, light waves and water waves.

Quotes

 * The wave equation behaves nicely in one dimension and in three dimensions but not in two dimensions. In one dimension, waves on a uniform string propagate without distortion. In three dimensions, waves in a homogeneous isotropic medium propagate in an undistorted way except for a spherical correction factor. However, in two dimensions, wave propagation is complicated and distorted. By its very nature, 2D processing never can account for events originating outside of the plane. As a result, 2D processing is broken up into a large number of approximate partial steps in a sequence of operations. These steps are ingenious, but they can never give a true image.