Approximate symmetry and solutions of the nonlinear Klein–Gordon equation with a small parameter

In this paper, the Lie approximate symmetry analysis is applied to investigate new solutions of the nonlinear Klein–Gordon equation with a small parameter. The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. The hyperbolic function method and Riccati equation method are employed to solve some of the obtained reduced ordinary differential equations. We construct new analytical solutions with a small parameter which is effectively obtained by the proposed method.