Mel'nikov Analysis of Homoclinic Chaos in a Perturbed sine-Gordon Equation

Details Mel'nikov Analysis of Homoclinic Chaos in a Perturbed sine-Gordon Equation Mel'nikov Analysis of Homoclinic Chaos in a Perturbed sine-Gordon Equation

1999-03-17

arxiv.org/abs/chao-dyn/9903023v2

Nonlinear Sciences

Chaotic Dynamics

25 pages, LaTeX, no figures

Scientific paper

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.

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