TY - JOUR
TI - Oscillations of dark solitons in trapped Bose-Einstein condensates
AU - Pelinovsky, D.E.
AU - Frantzeskakis, D.J.
AU - Kevrekidis, P.G.
JO - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
PY - 2005
VL - 72
TODO - 1
SP - null
PB - 
SN - 1539-3755, 1550-2376
TODO - 10.1103/PhysRevE.72.016615
TODO - Bose-Einstein condensates;  Dark soliton;  Radiative losses, Approximation theory;  Condensate treatment;  Heat radiation;  Oscillations, Solitons
TODO - 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. © 2005 The American Physical Society.
ER -