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:Journal of dynamics and differential equations 2009-12, Vol.21 (4), p.607-622
Main Authors: Manukian, Vahagn, Costanzino, Nicola, Jones, Christopher K. R. T., Sandstede, Björn
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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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:1040-7294
1572-9222
DOI:10.1007/s10884-009-9147-4