Here are some movies to illustrate the solutions of various wave equations. They are to accompany my textbook Elements of Astrophysics.
ocean.qt is a 7MB QuickTime format movie showing the evolution of a deep ocean wave. The initial conditions were a power-law spectrum Gaussian random displacement field with spectral index n=4. The initial velocity was set to zero, which is a bit unrealistic. If you look carefully at the first few frames you will see this causes a slightly weird effect, but after this it settles down. There is no self-interaction included here --- this is slightly unrealistic since, as shown, the wave amplitude is not really tiny --- and the wave was propagated simply by taking the initial conditions, forming the positive frequency part of the transform (see the appendix on dispersive waves) and then synthesizing the field at later times by multiplying the transform by exp(i omega(k) t).
ssb.qt (17MB) and ssb.mpg (4.2MB) and ssb.gif (32MB) show a 2-D scalar field with a W-shaped potential function undergoing spontaneous symmetry breaking.
packet.qt (7MB) and packet.mpg (2.8MB) and packet.gif (12MB) show the evolution of a wave packet of deep ocean waves.