2002/01/22 by Luca Salasnich, L. Salasnich, Alberto Parola +2 · 8 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Strong Light-Matter Interactions #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreva.65.043614
published as Phys. Rev. A 65, 043614 (2002) · 7 pages, 5 figures, to be published in Phys. Rev. A
arxiv created 2002/01/22 · openalex publication_date 2002/04/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent nonpolynomial nonlinear Schr"odinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D nonpolynomial Schr"odinger equation (2D NPSE) that models disk-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schr"odinger-like equations with different polynomial nonlinearities.