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Expected and Unexpected Solutions to the Stationary One-Dimensional Nonlinear Schrodinger Equation

Published

Author(s)

L D. Carr, Charles W. Clark, W P. Reinhardt

Abstract

We present all stationary solutions to the nonlinear Schrodinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schrodinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.
Citation
International Conference on Recent Progress in Many-Body Theories
Volume
15
Issue
10 and 11

Keywords

Bose-Einstein condensation, Jacobian elliptic functions, nonlinear Schroedinger equation, soliton

Citation

Carr, L. , Clark, C. and Reinhardt, W. (2001), Expected and Unexpected Solutions to the Stationary One-Dimensional Nonlinear Schrodinger Equation, International Conference on Recent Progress in Many-Body Theories, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=840093 (Accessed June 15, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created December 31, 2000, Updated October 12, 2021