Self-modulated nonlinear shear surface acoustic waves in crystals

Nonlinear, purely shear surface acoustic waves (SAW) are investigated in crystals. A set of such SAW described by N-soliton solutions of the nonlinear Schrödinger equation is obtained. The simplest of these waves was detected earlier by V. G. Mozhaev [Phys. Lett. A139, 333 (1989)]. Higher-order waves exhibit self-modulation along the direction of propagation with a spatial frequency proportional to U02 (U0 is the peak amplitude on the surface of a crystal), and a decrease in their amplitude with increasing depth can be nonmonotonic. The characteristic localization length for such SAW is proportional to U0−1. The excitation of waves of each order by synphase oscillations localized at the crystal surface is of a threshold nature. The stability of obtained waves to small changes in the boundary conditions and to a random perturbation of the oscillation phase in the initial section (which varies with the depth) is determined.

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