@article{3065393,
    title = "Oscillations of dark solitons in trapped Bose-Einstein condensates",
    author = "Pelinovsky, D.E. and Frantzeskakis, D.J. and Kevrekidis, P.G.",
    journal = "Physical Review E: Statistical, Nonlinear, and Soft Matter Physics",
    year = "2005",
    volume = "72",
    number = "1",
    issn = "1539-3755, 1550-2376",
    doi = "10.1103/PhysRevE.72.016615",
    keywords = "Bose-Einstein condensates;  Dark soliton;  Radiative losses, Approximation theory;  Condensate treatment;  Heat radiation;  Oscillations, Solitons",
    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. © 2005 The American Physical Society."
}