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The method of multiple scales is used to determine second-order uniform expansions for the displacements describing nonlinear plane waves propagating into an elastic half space. The material properties may be homogeneous or they may vary slowly in the direction of propagation. A discussion is presented for the interaction between dilatational and shear waves as well as the interaction between the nonlinearity and the heterogeneity. The present results and method of solution are compared with those obtained earlier for homogeneous and slightly heterogeneous media by using the analytic method of characteristics

NONLINEAR WAVES IN HOMOGENEOUS AND HETEROGENEOUS ELASTIC SOLIDS