Exact traveling wave solutions of the perturbed Klein–Gordon equation with quadratic nonlinearity in (1+1)-dimension, Part I: Without local inductance and dissipation effect

In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein–Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.