Homoclinic intersections and Mel'nikov method for perturbed sine-Gordon equation
نویسندگان
چکیده
منابع مشابه
Homoclinic Intersections and Mel'nikov Method for Perturbed sine -Gordon Equation
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.
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Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and ‘‘chaos cascade’’ referring to the embeddings of smaller scale chaos in larger scale chaos. 2003 Elsevier Ltd. All rights reserved.
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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 ...
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We give arguments for the existence of exact travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. Such solutions are allowed exactly by the energy balance of these terms, and can be observed experimentally e....
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ژورنال
عنوان ژورنال: Dynamical Systems
سال: 2001
ISSN: 1468-9367
DOI: 10.1080/14689360110063967