Invariants of two- and three-dimensional hyperbolic equations

We consider linear hyperbolic equations of the form u t t = ∑ i = 1 n u x i x i + ∑ i = 1 n X i ( x 1 , … , x n , t ) u x i + 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.