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On creation and evolution of dark solitons in Bose-Einstein condensates

V. A. Brazhnyi·A. M. Kamchatnov·V. V. Konotop
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Abstract

Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.

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V. A. Brazhnyi, A. M. Kamchatnov, V. V. Konotop. 2003-01-17. On creation and evolution of dark solitons in Bose-Einstein condensates. https://arxiv.org/abs/cond-mat/0301319

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