Nonlinear Love waves in a homogeneous layer overlying a homogeneous half-space

Abstract

In this article, the focus is on the propagation of Love waves in a solid layer overlying a solid half-space, assuming that both layer and half-space consist of nonlinear, isotropic, homogeneous, hyper-elastic, and generalized neo-Hookean materials, in addition to having different mechanical properties. As done by Love, displacements and stresses are assumed to be continuous at the interface between the layer and half-space, and the upper surface is to be free from traction, in addition to holding the radiation condition in the half-space. The method of multiple scales in the self modulation of the problem is used. Then, it is shown that the self modulation of the problem can be given by a nonlinear Schrödinger equation as a result of a balance between dispersion and nonlinearity. By using the coefficients of the nonlinear Schr¨odinger equation, the existence of the solitary waves is studied. In addition, the effects of the parameters of linear and nonlinear mediums on the functions of the wave propagation are studied.