Two-dimensional symmetry reduction of (2 + 1)-dimensional nonlinear Klein–Gordon equation

In this paper, one-dimensional optimal system of group invariant solutions of (2 + 1)-dimensional Klein–Gordon system is constructed. Then the classification of group invariant solutions is given out and the corresponding two-dimensional symmetry reduced equations are obtained. At last some symmetry transformations are gained in detail. Especially, we obtain the most general solution from a given solution by use of six variable one-parameter subgroups transformations.