Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity

Journal Article · Wed Feb 15 04:00:00 EST 2006 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PHYSREVE.73.0· OSTI ID:20778711

Sakaguchi, Hidetsugu ^[1]; Malomed, Boris A ^[2]

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1. Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580 (Japan)
2. Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We introduce a dynamical model of a Bose-Einstein condensate based on the two-dimensional Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value {approx_equal}0.47. The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable.

• OSTI ID: 20778711
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 73; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
AXIAL SYMMETRY
BOSE-EINSTEIN CONDENSATION
EQUATIONS
NONLINEAR PROBLEMS
PERTURBATION THEORY
RESONANCE
SCATTERING LENGTHS
SOLITONS
STABILITY
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
VORTICES