Envelope Periodic Solutions to One-Dimensional Gross-Pitaevskii Equation in Bose-Einstein Condensation

Usama Al Khawaja

Liu Shi-Kuo, Gao Bin, Zuntao Fu +1 more

In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross–Pitaevskii equation in Bose–Einstein condensates are obtained.

Jacopo Bellazzini, Luigi Forcella

Ashraf A. Abulseoud, Hala H. Alsayad, Tharwat M. El-Sherbini

Emmanuel Kengne, X. X. Liu, Boris A. Malomed +2 more

An effective Gross–Pitaevskii equation, which describes the dynamics of quasi-one-dimensional Bose–Einstein condensates in specific potential traps, is considered, and new families of exact solutions are reported, which include periodic and solitary waves. The solutions are applied to the description of BEC patterns trapped in optical-lattice potentials.

J. H. Huckans, Ian B. Spielman, B. Laburthe-Tolra +2 more

Rb Bose-Einstein condensate from a one-dimensional optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to numerical solutions of the Gross-Pitaevskii equation and classical calculations, with quantitative and qualitative agreement, respectively. The classical calculations predict that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase-space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.