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Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation

Chaos 19, 043105 (2009); doi:10.1063/1.3248269

Published 15 October 2009

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G. Gligorić,1 A. Maluckov,2 L. Salasnich,3 B. A. Malomed,4 and Lj. Hadžievski1
1Vinča Institute of Nuclear Sciences, P.O. Box 522, 11001 Belgrade, Serbia
2Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18001 Niš, Serbia
3Department of Physics “Galileo Galilei,” CNR-INFM and CNISM, University of Padua, Via Marzolo 8, 35131 Padua, Italy
4Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
The Bose–Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrödinger equation (NPSE). Both models are derived from the three-dimensional Gross–Pitaevskii equation (3D GPE). To produce “model 1” (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. “Model 2,” which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2—in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC. ©2009 American Institute of Physics
History: Received 9 June 2009; accepted 23 September 2009; published 15 October 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/043105/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.75.Lm
    Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations
  • 05.45.Yv
    Solitons
  • 42.50.Wk
    Mechanical effects of light on material media, microstructures and particles
  • 37.10.Jk
    Atoms in optical lattices
  • YEAR: 2009

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (20)
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  1. A. J. Leggett, Quantum Liquids (Oxford University Press, New York, 2006).
  2. V. M. Pérez-García, H. Michinel, and H. Herrero, Phys. Rev. A 57, 3837 (1998).
  3. A. E. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, Phys. Rev. Lett. 89, 110401 (2002).
  4. L. Salasnich, Laser Phys. 12, 198 (2002)
    5. L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 65, 043614 (2002)
    L. Salasnich, A. Parola, and L. Reatto, ibid. 70, 013606 (2004)
    L. Salasnich, A. Parola, and L. Reatto, ibid. 72, 025602 (2005)
    L. Salasnich and B. A. Malomed, ibid. 74, 053610 (2006)
    L. Salasnich, B. A. Malomed, and F. Toigo, ibid. 76, 063614 (2007).
  5. L. Salasnich, J. Phys. A: Math. Theor. 42, 335205 (2009).
  6. S. Sinha, A. Y. Cherny, D. Kovrizhin, and J. Brand, Phys. Rev. Lett. 96, 030406 (2006).
  7. L. Khaykovich and B. A. Malomed, Phys. Rev. A 74, 023607 (2006).
  8. S. De Nicola, B. A. Malomed, and R. Fedele, Phys. Lett. A 360, 164 (2006)
    9. S. De Nicola, R. Fedele, D. Jovanovic, B. Malomed, M. A. Man'ko, V. I. Man'ko, and P. K. Shukla, Eur. Phys. J. B 54, 113 (2006).
  9. R. Carretero-González, D. J. Frantzeskakis, and P. G. Kevrekidis, Nonlinearity 21, R139 (2008).
  10. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, Nature (London) 417, 150 (2002)
    11. see also K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, New J. Phys. 5, 73 (2003).
  11. S. L. Cornish, S. T. Thompson, and C. E. Wieman, Phys. Rev. Lett. 96, 170401 (2006).
  12. L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 66, 043603 (2002)
    13. L. Salasnich, ibid. 70, 053617 (2004)
    A. Muñoz Mateo and V. Delgado, Phys. Rev. Lett. 97, 180409 (2006)
    A. Muñoz Mateo and V. Delgado, Phys. Rev. A 77, 013617 (2008).
  13. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001)
    14. F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, Phys. Rev. A 64, 043606 (2001)
    G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop, and M. Salerno, Phys. Rev. E 66, 046608 (2002)
    R. Carretero-González and K. Promislow, Phys. Rev. A 66, 033610 (2002)
    N. K. Efremidis and D. N. Christodoulides, ibid. 67, 063608 (2003).
  14. G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, Phys. Rev. A 78, 063615 (2008).
  15. M. A. Porter, R. Carretero-González, P. G. Kevrekidis, and B. A. Malomed, Chaos 15, 015115 (2005)
    16. A. Maluckov, Lt. Hadžievski, and B. A. Malomed, Phys. Rev. E 76, 046605 (2007)
    R. Carretero-González, J. D. Talley, C. Chong, and B. A. Malomed, Physica D 216, 77 (2006).
  16. A. Maluckov, Lj. Hadžievski, B. A. Malomed, and L. Salasnich, Phys. Rev. A 78, 013616 (2008).
  17. G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, Phys. Rev. A 79, 053609 (2009).
  18. Y. Sivan, B. Ilan, and G. Fibich, Phys. Rev. E 78, 046602 (2008).
  19. M. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973)
    20. L. Bergé, Phys. Rep. 303, 259 (1998).
  20. G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, J. Phys. B 42, 145302 (2009).

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