ABSTRACT
We consider the perturbed sine-Gordon equation , where the external perturbation is small and slowly varying. We show that the initial value problem with an appropriate initial state close enough to the solitary manifold has a unique solution, which follows up to time and errors of order a trajectory on the solitary manifold. The trajectory on the solitary manifold is described by ODEs, which agree up to errors of order with Hamilton equations for the restricted to the solitary manifold sine-Gordon Hamiltonian.
Acknowledgments
My sincere gratitude goes to my PhD advisor Markus Kunze for the continuous support. I would like to thank Justin Holmer for helpful discussions.
Disclosure statement
No potential conflict of interest was reported by the author.