Periodic oscillations of dark solitons in parabolic potentials

Details Periodic oscillations of dark solitons in parabolic potentials Periodic oscillations of dark solitons in parabolic potentials

2007-05-08

arxiv.org/abs/0705.1016v1

Physics

Condensed Matter

Other Condensed Matter

20 pages, 3 figures

Scientific paper

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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