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.
This is a pre-print. The definitive version: ROTHOS, V.M., 2001. Homoclinic intersections and Mel'nikov method for perturbed sine-Gordon equation . Dynamical Systems, 16(3), pp.279-302, is available at: http://www.journalsonline.tandf.co.uk/openurl.asp?genre=journal&eissn=1468-9375.