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APS » Journals » Phys. Rev. Lett. » Volume 91 » Issue 23
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Phys. Rev. Lett. 91, 230402 (2003) [4 pages]

Bohr-Sommerfeld Quantization Condition for the Gross-Pitaevskii Equation

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V. V. Konotop1 and P. G. Kevrekidis2
1Centro de Física Teórica e Computacional and Departmento de Física, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisbon 1649-003, Portugal
2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

Received 6 May 2003; published 2 December 2003

The discrete spectrum of the nonlinear eigenvalue problem associated to the one-dimensional Gross-Pitaevskii equation with a smooth potential is studied in the quasiclassical limit. We particularly focus on the corrections to the Bohr-Sommerfeld quantization rule for the excited energy levels due to the nonlinearity. Explicit predictions are obtained analytically for these corrections and are supported by numerical computations.

© 2003 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.91.230402
DOI:
10.1103/PhysRevLett.91.230402
PACS:
03.65.Ge, 03.65.Sq
 
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