Mashkin, Timur (2020). Stability of the solitary manifold of the perturbed sine-Gordon equation. J. Math. Anal. Appl., 486 (2). SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-0813
Full text not available from this repository.Abstract
We study the perturbed sine-Gordon equation theta(tt) - theta(xx) + sin theta = F(epsilon, x), where F is of differentiability class C-n in epsilon and the first k derivatives vanish at epsilon = 0, i.e., partial derivative F-l(epsilon)(0, .) = 0 for 0 <= l <= k. We construct implicitly a virtual solitary manifold by deformation of the classical solitary manifold in n iteration steps. Our main result establishes that the initial value problem with an appropriate initial state epsilon(n)-close to the virtual solitary manifold has a unique solution, which follows up to time 1/((C) over tilde epsilon(k+1/2)) and errors of order epsilon(n) a trajectory on the virtual solitary manifold. The trajectory on the virtual solitary manifold is described by two parameters, which satisfy a system of ODEs. In contrast to previous works our stability result yields arbitrarily high accuracy as long as the perturbation F is sufficiently often differentiable. (C) 2020 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-330013 | ||||||||
| DOI: | 10.1016/j.jmaa.2020.123904 | ||||||||
| Journal or Publication Title: | J. Math. Anal. Appl. | ||||||||
| Volume: | 486 | ||||||||
| Number: | 2 | ||||||||
| Date: | 2020 | ||||||||
| Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||||||
| Place of Publication: | SAN DIEGO | ||||||||
| ISSN: | 1096-0813 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/33001 |
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