  Using the scalar curvature of the product manifold S^{2}X R and the complete
group classification of nonlinear Poisson equation on (pseudo) Riemannian
manifolds, we extend the previous results on symmetry analysis of homogeneous
wave equation obtained by H. Azad and M. T. Mustafa [H. Azad and M. T. Mustafa,
Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl., 333 (2007)
1180--1888] to nonlinear Klein-Gordon equations on the two-dimensional sphere.
