  We describe and characterize rigorously the chaotic behavior of the
sine-Gordon equation. The existence of invariant manifolds and the persistence
of homoclinic orbits for a perturbed sine--Gordon equation are established. We
apply a geometric method based on Mel'nikov's analysis to derive conditions for
the transversal intersection of invariant manifolds of a hyperbolic point of
the perturbed Poincare map.
