Nonlinear dispersive surface acoustic waves propagating on LiNbO3 single-crystal plates were studied. In order to control the dispersion, a thin SiO2 overlay was applied. Harmonic generation measurements in the crystals without SiO2 overlay show that the second-harmonic amplitude exceeds that of the fundamental wave when the initial wave amplitude exceeds 40 Å, and the spatial periodicity length of harmonic generation varies depending on power. In the samples with 500-Å-thick SiO2 coatings, no significant change of the periodicity length with power has been detected. In both cases we observed an increase of phase velocity with acoustic power. Comparison of the experimental data with the spectrum of Korteweg-de Vries solitons suggests the presence of surface acoustic wave solitons.