Approximate damped oscillatory solutions and error estimates for the perturbed Klein-Gordon equation

The influence of perturbation on traveling wave solutions of the perturbed Klein-Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis.