Non-linear bright solitary SH waves in a hyperbolically heterogeneous layer

Abstract

This work investigates the propagation of non-linear shear horizontal (SH) waves in a layer of finite depth overlying a rigid substratum. We assume that the layer consists of heterogeneous, isotropic, and incompressible hyper-elastic materials. By using the method of multiple scales, we show that the self-modulation of non-linear SH waves is governed by the non-linear Schrödinger (NLS) equation. Using known properties of solutions of NLS equation, we find that bright solitary SH waves can exist depending on the non-linear constitution of the layer. Consequently, not only the effect of the heterogeneity but also the effect of the non-linearity on the deformation field is discussed for these waves.