Physics – Condensed Matter
Scientific paper
2000-12-06
Phys. Rev. E 64, 056615 (2001)
Physics
Condensed Matter
12 pages, 18 figures
Scientific paper
10.1103/PhysRevE.64.056615
Using a standing light wave trap, 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.
Bronski Jared C.
Carr Lincoln D.
Carretero-González Ricardo
Deconinck Bernard
Kutz Nathan J.
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