title: Oscillations of dark solitons in trapped Bose-Einstein condensates.
abstract: 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.
authors.affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada.
authors.forename: Dmitry E
authors.initials: DE
authors.lastname: Pelinovsky
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis