Dark solitons in external potentials

Details Dark solitons in external potentials Dark solitons in external potentials

2006-10-31

arxiv.org/abs/cond-mat/0610881v1

Physics

Condensed Matter

Other Condensed Matter

39 pages, 10 figures

Scientific paper

10.1007/s00033-007-6120-0

We consider the persistence and stability of dark solitons in the Gross-Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable with exactly one real positive eigenvalue, while families at the minimum points are generally unstable with exactly two complex-conjugated eigenvalues with positive real part. This mechanism of destabilization of the black soliton is confirmed in numerical approximations of eigenvalues of the linearized GP equation and full numerical simulations of the nonlinear GP equation with cubic nonlinearity. We illustrate the monotonic instability associated with the real eigenvalues and the oscillatory instability associated with the complex eigenvalues and compare the numerical results of evolution of a dark soliton with the predictions of Newton's particle law for its position.

Affiliated with

Also associated with

No associations

Rating

Dark solitons in external potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dark solitons in external potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dark solitons in external potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-46952