Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation. (January 2015) - Ye, Caier; Zhang, Weiguo
Highlights: Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. Present the relations between the properties of traveling wave solutions and the perturbation coefficient. Obtain all explicit expressions of approximate damped oscillatory solutions. Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. Abstract: 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.