Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity
Lincoln D. CarrDepartment of Physics, University of Washington, Seattle, Washington 98195-1560Charles W. ClarkElectron and Optical Physics Division, National Institute of Standards and Technology, Technology Administration, U.S. Department of Commerce, Gaithersburg, Maryland 20899William P. ReinhardtDepartment of Chemistry, University of Washington, Seattle, Washington 98195-1700
2000en
ABI
Аннотация
All stationary solutions to the one-dimensional nonlinear Schr\"odinger 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 Schr\"odinger 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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