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

Vassilios M. Rothos
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Abstract

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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BibTeXRIS

Vassilios M. Rothos. 1999-07-20. Mel'nikov Analysis of Homoclinic Chaos in a Perturbed sine-Gordon Equation. https://arxiv.org/abs/chao-dyn/9903023

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