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

Lincoln D. Carr·Charles W. Clark·William P. Reinhardt
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Abstract

All stationary solutions to the one-dimensional nonlinear Schroedinger 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 grey 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.

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Lincoln D. Carr, Charles W. Clark, William P. Reinhardt. 2000-07-07. Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity. https://doi.org/10.1103/physreva.62.063610

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