Propagation of Love waves in a homogeneous layer overlying a heterogeneous half-space

The aim of this paper is, analytically and numerically, to deal with the nonlinear modulation of Love waves in a single-layered half-space. In this study, the propagation of Love waves in a solid half-space covered by a solid layer is considered. Both mediums contain nonlinear, isotopic, hyper-elastic, and generalized neo-Hookean materials. Additionally, the layer consists of homogeneous materials and the half-space involves heterogeneous materials. Heterogeneity varies with the thickness and is uniform in any direction parallel to the boundaries. Furthermore, the upper surface to be free from traction, and displacements and stresses to be continuous at the interface are assumed, in addition to holding the radiation condition in the half-space. It is noted that this problem corresponds to the improved version of Love wave propagation. An improvement is from linearity to nonlinearity and from homogeneity to heterogeneity. Therefore, the improved version of Love wave dispersion is obtained and the nonlinear modulation of Love waves is given by the nonlinear Schr & ouml;dinger equation. Moreover, the existence of bright and dark solitary Love wave solutions, as a result of balancing between dispersion and nonlinearity, is investigated. In this context, the effects of parameters of linear and nonlinear mediums are, graphically, given in details.