Group analysis for a linear hyperbolic equation arising from a quasilinear reducible system

The aim of this paper is to carry out infinitesimal group analysis for a second order linear hyperbolic equation in canonical form. To such a kind of equation one could be led in considering the hodograph transformation for a first order reducible system. In the first part of the paper we characterize the most general expression for the generator of the Lie group, which has an infinite dimensional algebra. Then we calculate the invariant surfaces in some special cases of interest, and point out the corresponding ordinary differential equations whose integration allows us to determine possible classes of solutions for the equation we are considering.