Abstract
A Rayleigh wave propagating along the boundary surface of an elastic half-space whose nonlinear deformation is described by the Murnaghan model is analyzed. Three simple equations of nonlinear motion for displacement and six new nonlinear wave equations for potentials are proposed. New approximate (first two approximations) solutions are obtained and discussed. It is shown that the second approximation includes the second harmonics of both traveling harmonic wave and its amplitude decreasing with depth and nonlinearly depends on the initial amplitude of the Rayleigh wave. The geometrically linear and nonlinear boundary conditions are written, and their difference is shown. Their role in the analysis of Rayleigh wave is discussed. A new nonlinear equation for the Rayleigh wave number is derived and analyzed
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