Classification of invariant wave equations

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 u_tt = F[u] and potential evolutionary equations u_xt = 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.