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.Comment: 20 pages, 3 figure

Kevrekidis, P. G.

Pelinovsky, D. E.

English

arXiv

This is the pre-published version harvested from arXiv.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

Pelinovsky, Dmitry

Kevrekidis, PG

ScholarWorks@UMass Amherst

Periodic oscillations of dark solitons in parabolic potentials

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

Periodic oscillations of dark solitons in parabolic potentials

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ScholarWorks@UMass Amherst

ScholarWorks@UMass Amherst