Transverse elastic waves behave differently in nonlinear isotropic andanisotropic media. Quadratically nonlinear coupling in the evolution equationsfor wave amplitudes is not possible in isotropic solids, but such a couplingmay occur for certain directions in anisotropic materials. We identify theexpression responsible for the coupling and we derive coupled canonicalevolution equations for transverse wave amplitudes in the case of two-fold andthree-fold symmetry acoustic axes. We illustrate our considerations by examplesfor a cubic crystal.
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