The dominant pulse forms, steepens, and radiates shorter waves. If the scale of the experiment and H are fairly large, these will be dominantly gravity waves. As these have group velocity greater than their phase velocity, they race out ahead of the dominant pulse. It is worth trying some creative lighting of this experiment. A slide projector with a slit slide can be directed at a small glancing angle onto the surface, so that the crests light up in a darkened room.
Undular bores refer to a change in mean fluid height, accompanied by a set of solitary waves.
Here, it is the wave pulses falling behind or ripples racing ahead that drain off the energy. A solitary wave or soliton is a single wave crest that propagates without any such radiation or linear dispersion. It is a perfect balance between the nonlinear steepening of the profile and the linear dispersion which tries to blunt it. Solitons are found in many wave media, and have great practical value in long-distance light transmission along an optical fiber. By defeating dispersion, solitons carry information more cleanly, and are thus worth money.