  The problem of the long wave runup on a beach is discussed in the framework
of the rigorous solutions of the nonlinear shallow-water theory. The key and
novel moment here is the analysis of the runup of a certain class of asymmetric
waves, the face slope steepness of which exceeds the back slope steepness.
Shown is that the runup height increases when the relative face slope steepness
increases whereas the rundown weakly depends on the steepness. The results
partially explain why the tsunami waves with the steep front (as it was for the
2004 tsunami in the Indian Ocean) penetrate deeper into inland compared with
symmetric waves of the same height and length.
