Periodic oscillations of dark solitons in parabolic potentials

@article{Pelinovsky2007PeriodicOO,
  title={Periodic oscillations of dark solitons in parabolic potentials},
  author={Dmitry E. Pelinovsky and Panayotis G. Kevrekidis},
  journal={arXiv: Other Condensed Matter},
  year={2007}
}
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… Expand

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