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