Geometrical Solutions Using Symmetries to Solve Wave Equation on Torus

In this paper determined the Lie’s symmetries of wave equation on torus. Symmetry algebras are found by using Lie’s classical method. We use different symmetries to obtain similarity reductions of wave equation by exploiting these symmetries, we perform similarity transformations, a powerful reduction for obtaining two new solutions of wave equation on torus. We investigated the new solutions of wave equation on a specific geometry surface torus.