One of the great achievements of 20th century mathematics is our new understanding of non-linear dynamics. A primary example is the SOLITON, which is a localized disturbance in a non-linear wave. In this animation you can see the collision of two solitons, and if you look closely you will see that the two "humps" literally bounce off of each other. The discovery of solitons has had a dramatic effect on our understanding of ocean waves, quantum physics and non-linear differential equations in general.
These images were created by Mathematica and converted into a multi-block gif image. The function displayed is an exact solution to the KdV Equation, the first non-linear PDE recognized as an integrable equation. Check out my soliton page for more information about solitons.