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Phys. Rev. A 62, 063610 (2000) [10 pages]

Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity

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L. D. Carr1,*, Charles W. Clark2, and W. P. Reinhardt1,2,3
1Department of Physics, University of Washington, Seattle, Washington 98195-1560
2Electron and Optical Physics Division, National Institute of Standards and Technology, Technology Administration, U.S. Department of Commerce, Gaithersburg, Maryland 20899
3Department of Chemistry, University of Washington, Seattle, Washington 98195-1700

Received 15 November 1999; revised 1 June 2000; published 15 November 2000

All stationary solutions to the one-dimensional nonlinear Schrödinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or gray density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schrödinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.

© 2000 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.62.063610
DOI:
10.1103/PhysRevA.62.063610
PACS:
03.75.Fi, 05.30.Jp, 05.45.Yv

*Author to whom correspondence should be addressed.

See Also

See Also: L. D. Carr, Charles W. Clark, and W. P. Reinhardt, Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity, Phys. Rev. A 62, 063611 (2000).

 
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