Oscillations of dark solitons in trapped Bose-Einstein condensates

Details Oscillations of dark solitons in trapped Bose-Einstein condensates Oscillations of dark solitons in trapped Bose-Einstein condensates

2005-03-29

arxiv.org/abs/cond-mat/0503657v1

Physics

Condensed Matter

Other Condensed Matter

13 pages, 3 figures

Scientific paper

10.1103/PhysRevE.72.016615

We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multi-scale expansion method in the limit when the potential trap is flat. The first-order approximation predicts a uniform frequency of oscillations for the dark soliton of arbitrary amplitude. The second-order approximation predicts the nonlinear growth rate of the oscillation amplitude, which results in decay of the dark soliton. The results are compared with the previous publications and numerical computations.

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