1999/11/30 by Lincoln D. Carr, Charles W. Clark, William P. Reinhardt · 2 citations
Physics and Astronomy · #cond-mat #nlin.SI
paper · pdf · doi:10.1103/physreva.62.063610
published as Phys. Rev. A 62, 063610 (2000) · 11 pages, 7 figures -- revised version
arxiv created 2000/07/07 · arxiv updated 2009/11/30
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.