waves caused by bodies falling in water

webdreamer

I've been trying to find equations that model the effect on water of something falling onto it (a pebble for example), without much success. Do you know them or where I can find them? It's such a common thing, it suppose it's not that hard, I just don't know where to look. It's of course a wave, but the wavelength gets smaller as it gets away from the "epicenter", sort of speak.
I also would like to know how it starts propagating, I mean, does the amplitude of the wave grows at first, as the pebble goes deeper, does it send several waves?

I'm trying to simulate the effect of bodies falling on water for a game.