Aren't you glad we don't generally have to worry about nonlinearities
in the propagation of our waves (through space or along transmission
lines)? (Well, maybe you do if you aren't using a reasonable model
for your lines...) Following is from an e-newsletter I get:

"Did you know that a wave breaks when the water underneath
supporting the wave is only about 1.3 times as deep as the
wave is high? When that happens, the water at the crest is
moving faster than the water below. Most often, waves break
in shallow water near the shore, but waves may also break
father off if the wave is high enough."