Two-dimensional gap solitons in elliptic-lattice potentials

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.033805· OSTI ID:21408489

Yingji, He ^[1]; Malomed, Boris A ^[2]; Bambi, Hu ^[1]

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1. Department of Physics, Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong (Hong Kong)
2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center): elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly uniform to double-peaked and, eventually, to the DS. In the attractive model, there exist only DSs in the oval trough, while EASs are not found. All such solitons without the angular momentum (l=0) are fully stable. For l{ne}0, vortical solitons--both EASs with a sufficiently large norm (in the repulsive model) and DSs (in models with both signs of the nonlinearity)--are quasistable, exhibiting rocking motion in the elliptic trough (we consider the cases of l=1 and l=2). At smaller values of the norm, the vortical annular solitons (in the repulsive model) are unstable. Stable fundamental solitons trapped in the central potential well are investigated, too, in both the attractive and repulsive models, by means of the variational approximation and numerical methods.

• OSTI ID: 21408489
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
APPROXIMATIONS
CALCULATION METHODS
CENTRAL POTENTIAL
DENSITY
DISTRIBUTION
EQUATIONS
NONLINEAR PROBLEMS
PHYSICAL PROPERTIES
POTENTIALS
QUASI PARTICLES
SOLITONS
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS