have you ever thrown a rock into a still pond, stared at the concentric waves for a while and realized that the farther the waves travel, the smaller their crests seem to get? in this talk, we'll discuss a class of equations that, like the water waves in a pond, disperse. we'll discuss common techniques to study existence and qualitative properties of solutions to nonlinear dispersive pdes using equations that model the strong nuclear force: the dirac-klein-gordon system.