Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-07-09
Laser Physics 12, 37-42 (2002)
Physics
Condensed Matter
Statistical Mechanics
13 pages, 5 figures, presented at the 10th International Laser Physics Workshop (LPHYS'01), Moscow, Russia, July 3-7, 2001
Scientific paper
The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated Schr\"odinger equation and those which do not have linear counterpart. Analytical and numerical results support an existence condition for the solutions of the first class in terms of the ratio between their proper frequency and the corresponding linear eigenvalue. For one-dimensional confined systems, we show that solutions without linear counterpart do exist in presence of a multi-well external potential. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.
D'Agosta Roberto
Malomed Boris A.
Presilla Carlo
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