This is the wave by fans. Does it satisfy the wave equation?
With the football stadium wave, the thing is that each person acts individually and everyone behaves differently. If you assume they react all under the same conditions (e.g. they see their direct neighbor standing up), with equal reaction time (a key quantity here) and they all move up and down in the same manner (for example like one smoothed out cosine bump), then you can view it as a wave on a torus shaped grid, their seats being the grid points. I can't see which particular equation that system will fulfill though, if you make some sort of continuum limit.
This video is somewhat related (and also pretty cool). It gives a straightforward idea of the field concept, emerging through distinct living agents.