Exact solutions of a (2+1)-dimensional nonlinear Klein-Gordon equation

The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differe ntial equations of second order and their solutions by a singularity analys is are classified. In particular, it has been shown that whenever they have the Painleve property, they can be transformed to standard forms by Moebiu s transformations of dependent variable and arbitrary smooth transformation s of independent variable whose solutions, depending on the values of param eters, are expressible in terms of either elementary functions or Jacobi el liptic functions.