Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries

‎This paper obtains the exact solutions of the wave equation as a secondorder partial differential equation (PDE)‎. ‎We are going to calculate polynomial and nonpolynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is presented and this extended to the construction of related polynomials‎.