Recent observations of Saturn's rings by the Cassini spacecraft show strong wakes excited by the satellite, Pan, which orbits inside the Encke gap. I will present a nonlinear fluid model of the wakes that models ring particle collisions with an effective viscosity. The model describes the nonlinear wake peaks as a shock structure that is similar to the shock wave solution to the Burgers equation. I will also present N-body simulations of satellite wakes in Saturn's rings that display a periodic gravitational instability which is induced by the collisional dynamics in the wake.