Homoclinic intersections and Mel'nikov method for perturbed sine-Gordon equation

Rothos, Vassilios M.

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Homoclinic intersections and Mel'nikov method for perturbed sine-Gordon equation

preprint

posted on 2006-01-17, 10:41 authored by Vassilios M. Rothos

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.

History

School

Science

Department

Mathematical Sciences

Pages

343470 bytes

Publication date

2001

Notes

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.