Exact travelling wave solutions for four forms of nonlinear Klein–Gordon equations

A variable separated equation and its solutions are used to construct the exact travelling wave solutions for four forms of nonlinear Klein–Gordon equations. The solutions previously obtained by the tanh and sech method are recovered. New and more exact travelling wave solutions including solitons, kink and anti-kink, bell and anti-bell solitary wave solutions, periodic solutions, singular solutions and exponential solutions are found.