Oscillations of dark solitons in trapped Bose-Einstein condensates.
We consider a one-dimensional defocusing Gross-Pitaevskii equation with a parabolic potential. Dark solitons oscillate near a center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multiscale 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 previous publications and numerical computations.
Pelinovsky
Dmitry E
DE
Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada.
Frantzeskakis
D J
DJ
Kevrekidis
P G
PG