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arXiv · 0907.2231

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

Vahagn Manukian·Nick Costanzino·Christopher K. R. T. Jones·Bjorn Sandstede
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Abstract

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.

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Vahagn Manukian, Nick Costanzino, Christopher K. R. T. Jones, Bjorn Sandstede. 2009-07-13. Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations. https://doi.org/10.1007/s10884-009-9147-4

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