G. E. Astrakharchik, L. P. Pitaevskii
We study the solitonic Lieb II branch of excitations in one-dimensional Bose gas in homogeneous and trapped geometry. Using Bethe ansatz equations we calculate the "number of particles" and the "effective mass" of a soliton. The frequency of oscillations in a harmonic trap is calculated. It changes continuously from its "soliton-like" value \omega/sqrt(2) in the high density mean field regime to \omega in the low density Tonks-Girardeau regime with \omega the frequency of the harmonic trapping. The phase jump of the order parameter is calculated.
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http://arxiv.org/abs/1210.8337
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