Finite-well potential in the 3D nonlinear Schrödinger equation: application to Bose-Einstein condensation
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Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schrödinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.
PACS.45.05.+x General theory of classical mechanics of discrete systems 05.45.-a Nonlinear dynamics and chaos 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties
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- Y.S. Kivshar, G.P. Agrawal, Optical Solitons - From Fibers to Photonic Crystals (Academic Press, San Diego, 2003) Google Scholar
- V.E. Zakharov, A.B. Shabat, Sov. Phys. JETP 34, 62 (1972); V.E. Zakharov, A.B. Shabat, Sov. Phys. JETP 37, 823 (1973) Google Scholar
- P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, R. Carretero-González, Phys. Rev. Lett. 93, 080403 (2004); D. Mihalache, D. Mazilu, I. Towers, B.A. Malomed, F. Lederer, Phys. Rev. E 67, 056608 (2003); P.M. Lushnikov, M. Saffman, Phys. Rev. E 62, 5793 (2000); N. Aközbek, S. John, Phys. Rev. E 57, 2287 (1998); D.E. Edmundson, Phys. Rev. E 55, 7636 (1997); N. Akhmediev, J.M. Soto-Crespo, Phys. Rev. A 47, 1358 (1993) CrossRefADSGoogle Scholar
- L.I. Schiff, Quantum Mechanics, 3rd edn. (McGraw-Hill, New York, 1968) Google Scholar
- H. Goldstein, Classical Mechanics, 2nd edn. (Addison Wesley, Reading, 1980) Google Scholar