General theory for the spectral evolution of nonlinear Rayleigh waves

The spectral theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569–2575 (1992)] for nonlinear Rayleigh waves in isotropic solids is generalized to include fields with nonperiodic waveforms and nonplanar spatial dependencies. Model equations for cylindrical waves and diffracting beams that have been used in previous work, and which were obtained in an ad hoc manner, are derived here rigorously from first principles. The present theory for plane waves, which is derived using Hamiltonian formalism, is shown to be equivalent to the theory obtained by Parker [Int. J. Eng. Sci. 26, 59–75 (1988)], whose derivation is based on a different approach.