Pulsed, plane, nonlinear Rayleigh waves in isotropic solids are investigated with numerical solutions of the coupled spectral equations derived by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569 (1992)]. Calculations of waveform evolution are presented as functions of distance from the source and depth within the solid. For the case of weak nonlinearity (characteristic absorption length on the order of the shock formation distance), self-demodulation of tone bursts is investigated. Self-demodulation refers to the nonlinear generation of a low-frequency waveform by a high-frequency pulse. Comparisons are made with the analogous process in fluids. Whereas demodulated Rayleigh and acoustic waveforms have similar shapes, the demodulated Rayleigh waveforms have substantially smaller relative amplitudes. The difference in amplitude is due to the frequency dependence of the nonlinearity coefficient matrix for Rayleigh waves. For the case of strong nonlinearity, shock formation is investigated in a variety of transient waveforms. Via comparison with acoustic waveform evolution in fluids, precursors generated by certain Rayleigh waveforms are identified as consequences of nonlocal nonlinearity. [Work supported by DOE, ONR, and NSF.]