Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE). We are going to calculate polynomial and non-polynomial 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.