Homoclinic intersections and Mel'nikov method for perturbed sine-Gordon equation
preprintposted on 17.01.2006, 10:41 authored by Vassilios M. Rothos
We describe and characterize rigorously the homoclinic structure of the perturbed sine- Gordon equation under periodic boundary conditions. The existence of invariant manifolds for a perturbed sine-Gordon equation is established. Mel'nikov method, together with geometric analysis are used to assess the persistence of the homoclinic orbits under bounded and time-periodic perturbations.
- Mathematical Sciences