The theory for nonlinear surface acoustic waves in crystals developed using Hamiltonian mechanics [Hamilton, Il'inskii, and Zabolotskaya, J. Acoust. Soc. Am. 105, 639 (1999)] is modified to account for piezoelectric material properties. The derived spectral evolution equations permit analysis of nonlinear surface wave propagation along a cut surface of any orientation with respect to the crystallographic axes and for piezoelectric crystals with any symmetry. Numerical simulations of waveform distortion in the particle velocity and electric field components are presented for surface wave propagation in Y-cut lithium niobate along the X- and Z-crystallographic axes. The influence of piezoelectricity is illustrated by comparing the nonlinear evolution of waveforms along a surface bounded by a vacuum (free space) and an ideal conductor (short circuit). Contributions to the nonlinearity from elasticity, piezoelectricity, electrostriction, and dielectricity are quantified separately for the two boundary conditions.
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