Abstract
Evolution equations are derived for nonlinear Rayleigh waves on the surface of an isotropic solid. Two evolution equations are derived, one in terms of the real horizontal displacement component, and the other in terms of a complex displacement variable. The equations are derived from the theoretical model developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569–2575 (1992)]. To simplify the present analysis, not all nonlinear terms are included. However, the simplified model is shown to provide a good approximation of the nonlinear effects predicted by the complete model. Moreover, the present analysis can be extended to include the remaining nonlinear terms. Numerical solutions obtained by solving the complex evolution equation in the time domain are compared with frequency domain calculations.
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