Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

Journal Article · Tue Dec 15 00:00:00 EST 2009 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.3248269· OSTI ID:21347371

Gligoric, G; Hadzievski, Lj ^[1]; Maluckov, A ^[2]; Salasnich, L ^[3]; Malomed, B A ^[4]

---

1. Vinca Institute of Nuclear Sciences, P.O. Box 522, 11001 Belgrade (Serbia)
2. Faculty of Sciences and Mathematics, University of Nis, P.O. Box 224, 18001 Nis (Serbia)
3. Department of Physics 'Galileo Galilei', CNR-INFM and CNISM, University of Padua, Via Marzolo 8, 35131 Padua (Italy)
4. Department 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 Schroedinger 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.

• OSTI ID: 21347371
• Journal Information: Chaos (Woodbury, N. Y.), Vol. 19, Issue 4; Other Information: DOI: 10.1063/1.3248269; (c) 2009 American Institute of Physics; ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
MATHEMATICAL SOLUTIONS
NUMERICAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION
SOLITONS
THREE-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
WAVE EQUATIONS