D.E. Pelinovsky, D.J. Frantzeskakis, and P.G. Kevrekidis

Oscillations of dark solitons in trapped Bose-Einstein condensates

Physical Review E 72, 016615 (2005)

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 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.

Keywords:
DEFOCUSING NONLINEAR SCHRODINGER EQUATION, DARK SOLITONS, HARMONIC POTENTIALS, NONLINEAR DYNAMICS, PERTURBATION THEORY FOR DARK SOLITONS, OSCILLATIONS AND RADIATIVE DAMPING OF DARK SOLITONS