  Dispersive effects during long wave run-up on a plane beach are studied. We
take an advantage of experimental data collection of different wave types
(single pulses, sinusoidal waves, bi-harmonic waves, and frequency modulated
wave trains) and simulate their run-up using two models: (i) non-dispersive
nonlinear shallow water theory and (ii) dispersive Boussinesq type model based
on the modified Peregrine system. It is shown, that for long positive pulses,
dispersive effects are not so important and nonlinear shallow water theory can
be used. However, for periodic sinusoidal and bi-harmonic pulses of the same
period, the dispersive effects result in significant wave transformation during
its propagation, but do not have a strong impact on its maximal run-up height.
Overall, for maximum wave run-up height, we could not find a preference of
dispersive model against the nondispersive one, and, therefore, suggest using
nonlinear shallow water model for long wave run-up height estimation.
