Nonlinear evolution equations for degenerate transverse waves in anisotropic elastic solids

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