Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations

The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pu...

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Bibliographic Details
Published in:arXiv.org 2009-07
Main Authors: Manukian, Vahagn, Costanzino, Nick, Christopher K R T Jones, Sandstede, Bjorn
Format: Article
Language:English
Subjects:
Bifurcations
Fields (mathematics)
Perturbation theory
Singular perturbation
Online Access:Get full text
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Summary:The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov--Schmidt reduction through Lin's method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.
ISSN:2331-8422
DOI:10.48550/arxiv.0907.2231