Periodic oscillations of dark solitons in parabolic potentials

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We reformulate the Gross-Pitaevskii equation with an external parabolic potential as a discrete dynamical system, by using the basis of Hermite functions. We consider small amplitude stationary solutions with a single node, called dark solitons, and examine their existence and linear stability. Furthermore, we prove the persistence of a periodic motion in a neighborhood of such solutions. Our results are corroborated by numerical computations elucidating the existence, linear stability and dynamics of the relevant solutions.
20 pages, 3 figures

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http://salesiana.dossiersoluciones.com/handle/123456789/128561

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.1016
 http://arxiv.org/abs/0705.1016

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arXiv