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

Published

January 1, 2001

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

Pub Type

Journals

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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 July 18, 2024)