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Oscillations of dark solitons in trapped Bose-Einstein condensates

Dmitry E. Pelinovsky·D. J. Frantzeskakis·P. G. Kevrekidis
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Abstract

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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Dmitry E. Pelinovsky, D. J. Frantzeskakis, P. G. Kevrekidis. 2005-03-29. Oscillations of dark solitons in trapped Bose-Einstein condensates. https://doi.org/10.1103/physreve.72.016615

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