2001/06/12 by Bernard Deconinck, Béla A. Frigyik, Bela A. Frigyik +4
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #Condensed Matter (cond-mat) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Strong Light-Matter Interactions #cond-mat #math-ph #math.AP #math.MP #nlin.PS
paper · pdf · doi:10.48550/arxiv.cond-mat/0106231
37 pages, 27 figures, with an appendix by J. C. Bronski
arxiv created 2001/06/12 · openalex publication_date 2001/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cubic nonlinear Schrodinger equation with a lattice potential is used to\nmodel a periodic dilute gas Bose-Einstein condensate. Both two- and\nthree-dimensional condensates are considered, for atomic species with either\nrepulsive or attractive interactions. A family of exact solutions and\ncorresponding potential is presented in terms of elliptic functions. The\ndynamical stability of these exact solutions is examined using both analytical\nand numerical methods. For condensates with repulsive atomic interactions, all\nstable, trivial-phase solutions are off-set from the zero level. For\ncondensates with attractive atomic interactions, no stable solutions are found,\nin contrast to the one-dimensional case.\n