  The problem of tsunami wave run-up on a beach is discussed in the framework
of the rigorous solutions of the nonlinear shallow-water theory. We present an
analysis of the run-up characteristics for various shapes of the incoming
symmetrical solitary tsunami waves. It will be demonstrated that the extreme
(maximal) wave characteristics on a beach (run-up and draw-down heights, run-up
and draw-down velocities and breaking parameter) are weakly dependent on the
shape of incident wave if the definition of the significant wave length
determined on the 2/3 level of the maximum height is used. The universal
analytical expressions for the extreme wave characteristics are derived for the
run-up of the solitary pulses. They can be directly applicable for tsunami
warning because in many case the shape of the incident tsunami wave is unknown.

Atmospheric and Oceanic Physics;Geophysics