2004/04/14 by A. M. Kamchatnov, V. S. Shchesnovich · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat.soft
paper · pdf · doi:10.1103/physreva.70.023604
published as Phys. Rev. A 70, 023604 (2004) · 20 pages, 4 figures
arxiv created 2004/04/14 · openalex publication_date 2004/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Gross-Pitaevskii equation for a Bose-Einstein condensate confined in an elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to a description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low-density limit our results reproduce the known formulas. In the high-density case our description of solitons goes beyond the standard approach based on the nonlinear Schr"odinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. The Korteweg--de Vries equation for weakly nonlinear waves is derived and the existence of bright solitons on a constant background is predicted for a dense enough condensate with a repulsive interaction between the atoms.