Invariants of two- and three-dimensional hyperbolic equations

We consider linear hyperbolic equations of the formutt=∑i=1nuxixi+∑i=1nXi(x1,…,xn,t)uxi+T(x1,…,xn,t)ut+U(x1,…,xn,t)u. We derive equivalence transformations which are used to obtain differential invariants for the cases n=2n=2 and n=3n=3. Motivated by these results, we present the general results for the n  -dimensional case. It appears (at least for n=2n=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.