Integration of two simultaneous partial differential equations (PDEs) converts initial disturbances (the points on the blue line) into stable solitonic "blips" (the red points) with speeds related to heights.

Integration of two simultaneous partial differential equations (PDEs) converts initial disturbances (the points on the blue line) into stable solitonic "blips" (the red points) with speeds related to heights. One, two, or more distinct blips are generated from different initial conditions. The filled red line attempts quadratic interpolation of the red points, but sometimes disappears or becomes negative because the points are on a spiky function. Both equations give similar results. They are related to a third "modulated Gaussian" equation that is shown but that requires further research.

http://demonstrations.wolfram.com/BlipSolitons/