## 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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### References:

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