Homoclinic orbits for the perturbed sine‐Gordon equation

In this work, we study the persistence of a homoclinic orbit of the sine‐Gordon equation under diffusive and driven perturbations. An analytic perturbation method based on time‐dependent scattering theory, together with Fredholm theory, is used to establish persistence. The estimates are given in space‐time function spaces, with a certain time decay required for the existence of a homoclinic orbit. © 2000 John Wiley & Sons, Inc.