Periodic oscillations of dark solitons in parabolic potentials
Other Condensed Matter
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.0705.1016,
title = {Periodic oscillations of dark solitons in parabolic potentials},
author = {D. E. Pelinovsky and P. G. Kevrekidis},
journal= {arXiv preprint arXiv:0705.1016},
year = {2007}
}
Comments
20 pages, 3 figures