Publication Date
2007
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.
Recommended Citation
Pelinovsky, Dmitry and Kevrekidis, PG, "Periodic oscillations of dark solitons in parabolic potentials" (2007). Mathematics and Statistics Department Faculty Publication Series. 1077.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1077
Comments
This is the pre-published version harvested from arXiv.