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Abstract
The general scheme which was developed for balance equations of arbitrary order is applied to determine isovector fields (infinitesimal generators) of symmetry groups (Lie groups) related to field equations describing the propagation of plane waves in heterogeneous and anisotropic hyperelastic materials. This approach yields in principle all classes of materials (strain energy functions) admitting possible symmetry groups. Homogeneous and isotropic cases are also treated. Ordinary differential equations which determine similarity solutions corresponding to some symmetry groups are given.
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