Fig. 11

Collision of two pulses from direct numerical simulation with parameters as in Figure 10. Columns A and C show u and a, respectively. Column B shows the $u=h$ interfaces, velocities (arrows to scale but enlarged by a factor of four), and dotted centerlines as visual guides. See also the video in Additional file 7. Column D predicts to $O(c^3)$ the shape of a traveling pulse for different c.