Phys. Rev. A 62, 063611 (2000) [10 pages]Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearityReceived 15 November 1999; revised 1 June 2000; published 15 November 2000 All stationary solutions to the one-dimensional nonlinear Schrödinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper treated the repulsive case. Our solutions take the form of bounded, quantized, stationary trains of bright solitons. Among them are two uniquely nonlinear classes of nodeless solutions, whose properties and physical meaning are discussed in detail. The full set of symmetry-breaking stationary states are described by the Cn character tables from the theory of point groups. We make experimental predictions for the Bose-Einstein condensate, and show that, though these are the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces surprising phenomena. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.62.063611
DOI:
10.1103/PhysRevA.62.063611
PACS:
03.75.Fi, 05.30.Jp, 05.45.Yv
See AlsoSee Also: L. D. Carr, Charles W. Clark, and W. P. Reinhardt, Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity, Phys. Rev. A 62, 063610 (2000). |
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