  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.
