An efficient systematic procedure is provided for symbolic computation of Liegroups of equivalence transformations and generalized equivalencetransformations of systems of differential equations that contain arbitraryelements (arbitrary functions and/or arbitrary constant parameters), using thesoftware package GeM for Maple. Application of equivalence transformations tothe reduction of the number of arbitrary elements in a given system ofequations is discussed, and several examples are considered. Firstcomputational example of a generalized equivalence transformation where thetransformation of the dependent variable involves the arbitrary constitutivefunction is presented. As a detailed physical example, a three-parameter family of nonlinear waveequations describing finite anti-plane shear displacements of an incompressiblehyperelasic fiber-reinforced medium is considered. Equivalence transformationsare computed and employed to radically simplify the model for an arbitraryfiber direction, invertibly reducing the model to a simple form thatcorresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systemsof differential equations containing arbitrary elements.
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