Classification of invariant wave equations

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Abstract
In this paper we characterize the possible symmetry groups of wave equations and certain evolutionary generalizations, in a single time variable and one or more spatial variables. Furthermore, we describe a complete classification of two-dimensional wave equations utt=F[u] and potential evolutionary equations uxt=F[u] having a point or contact symmetry group. The results rely on Lie’s classification of planar transformation groups and their relative differential invariants.

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