Periodic oscillations of dark solitons in parabolic potentials
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 …