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On Discrete Symmetries of Differential Equations

The determination of the continuous symmetries of differential equations follows a well known algorithm, and is reduced to solution of a set of linear equations; this is based on considering infinitesimal generators of the symmetries, so that the method does not extend to discrete symmetries. In this paper, we present a method to determine discrete symmetries in a certain class by means of a linear system, although this is considerably more difficult to solve than the one connected with continuous symmetries. We also consider the inverse (and simpler) problem of determining the most general equation admitting a given discrete symmetry. In the last part, we consider a number of examples, dealing in particular with symmetries of relevance to physics.