NONLINEAR DARK SOLITARY SH WAVES IN A HETEROGENEOUS LAYER

NONLINEAR DARK SOLITARY SH WAVES IN A HETEROGENEOUS LAYER

D. Demirku┼č

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Abstract

In this study, we consider the nonlinear propagation of shear horizontal (SH) waves in a layer of nite thickness. The materials of the layer are assumed to be heterogeneous, isotropic, and generalized neo-Hookean. We assume that heterogeneity varies only with the thickness and we choose hyperbolic functions for heterogeneity type. We also assume that the traction is free on the upper surface of the layer. Furthermore, the lower boundary is rigidly xed. Using a perturbation method and keeping the balance of the nonlinearity and the dispersion in the analysis, we show that the self-modulation of nonlinear SH waves can be given by the nonlinear Schrodinger (NLS) equation. Using well known solutions of NLS equation, we nd that the dark solitary SH waves can exist depending on the nonlinear constitution of the layer. Consequently, the e ects of the heterogeneity and the nonlinearity on the deformation eld are considered for these waves.

Keywords

Nonlinear SH waves, dark solitary waves, rigid substratum, heterogeneity.