2000/12/06 by Jared C. Bronski, J. C. Bronski, Lincoln D. Carr +9
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Elliptic function #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear system #Periodic potential #Phase function #Physics #Quantum mechanics #Schrödinger equation #Stability (learning theory) #Standing wave #Strong Light-Matter Interactions #cond-mat
paper · pdf · doi:10.1103/physreve.64.056615
published as Phys. Rev. E 64, 056615 (2001) · 12 pages, 18 figures
arxiv created 2000/12/06 · openalex publication_date 2001/10/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using a standing light wave potential, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr"odinger equation nor in the integrable nonlinear Schr"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.