Run-up of solitary waves on slopes with different profiles

The problem of sea-wave run-up on a beach is discussed within the framework of exact solutions of a nonlinear theory of shallow water. Previously, the run-up of solitary waves with different forms (Gaussian and Lorentzian pulses, a soliton, special-form pulses) has already been considered in the literature within the framework of the same theory. Depending on the form of the incident wave, different formulas were obtained for the height of wave run-up on a beach. A new point of this study is the proof of the universality of the formula for the maximum height of run-up of a solitary wave on a beach for the corresponding physical choice of the determining parameters of the incident wave, so that the effect of difference in form is eliminated. As a result, an analytical formula suitable for applications, in particular, in problems related to tsunamis, has been proposed for the height of run-up of a solitary wave on a beach.