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Nonlinear surface modes in crystals. (English) Zbl 0762.73020

Summary: We examine theoretically the influence of nonlinearity on characteristics of the shear-horizontal surface waves in crystals. We demonstrate that the dynamics of the system may be described in the framework of an effective nonlinear parabolic equation, the so-called nonlinear Schrödinger equation. We predict the existence of a set of nonlinear surface modes; the simplest mode is described by a sech-type function of \(z\), \(z\) being the distance from the surface. The higher order modes have internal frequencies stimulated by the nonlinearity. All these modes decay in the crystal as \(u_ 0exp(-z/z_ 0)\), \(z\gg z_ 0\sim u_ 0^{-1}\), where \(u_ 0\) is the wave amplitude at the surface. The creation of the modes from an arbitrary surface excitation has a threshold.

MSC:

74J15 Surface waves in solid mechanics
74E10 Anisotropy in solid mechanics
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