Soliton for nonlinear Rayleigh surface waves on homogeneous isotropic materials

We reinvestigate the steady propagation of nonlinear Rayleigh surface waves on homogeneous isotropic materials by the method of multiple scales. We find an explicit form for the steady propagation of nonlinear Rayleigh surface waves in terms of the Jacobi elliptic functions using a parametric excitation model. We show theoretically that finite-amplitude Rayleigh waves can propagate as a solitary pulse or shock on a homogeneous isotropic solid. In this study, we suggest that the propagation of nonlinear Rayleigh surface waves on viscoelastic materials can be described by the complex Ginzburg–Landau equation.