Invariants of two- and three-dimensional hyperbolic equations

We consider linear hyperbolic equations of the form u(tt) = Sigma(n)(i=1) u(xixi) + Sigma(n)(i=1) X(i)(x(1).....x(n).t) u(xi) + T (x(1).....x(n).t)u(t) + U(x(1)......x(n).t)u. We derive equivalence transformations which are used to obtain differential invariants for the cases n=2 and n=3. Motivated by these results, we present the general results for the n-dimensional case. It appears (at least for n=2) that this class of hyperbolic equations admits differential invariants of order one, but not of order two. We employ the derived invariants to construct interesting mappings between equivalent equations.