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arXiv · 0705.1016

Periodic oscillations of dark solitons in parabolic potentials

D. E. Pelinovsky·P. G. Kevrekidis
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Abstract

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.

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D. E. Pelinovsky, P. G. Kevrekidis. 2007-05-08. Periodic oscillations of dark solitons in parabolic potentials. https://arxiv.org/abs/0705.1016

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