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Title

Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities

AuthorsGómez-Gardeñes, Jesús; Malomed, B. A.; Floría, Luis Mario; Bishop, A. R.
KeywordsOptical solitons
Bose-Einstein condensation
Optical self-focusing
Lattice theory
Optical vortices
Issue DateSep-2006
PublisherAmerican Physical Society
CitationPhysical Review - Section E - Statistical Nonlinear and Soft Matter Physics 74(3): 036607.1-036607.10 (2006)
AbstractAn anisotropic lattice model in two spatial dimensions, with on-site and intersite cubic nonlinearities (the Salerno model), is introduced, with emphasis on the case in which the intersite nonlinearity is self-defocusing, competing with on-site self-focusing. The model applies, for example, to a dipolar Bose-Einstein condensate trapped in a deep two-dimensional (2D) optical lattice. Soliton families of two kinds are found in the model: ordinary ones and cuspons, with peakons at the border between them. Stability borders for the ordinary solitons are found, while all cuspons (and peakons) are stable. The Vakhitov-Kolokolov criterion does not apply to cuspons, but for the ordinary solitons it correctly identifies the stability limits. In direct simulations, unstable solitons evolve into localized pulsons. Varying the anisotropy parameter, we trace a transition between the solitons in 1D and 2D versions of the model. In the isotropic model, we also construct discrete vortices of two types, on-site and intersite centered (vortex crosses and squares, respectively), and identify their stability regions. In simulations, unstable vortices in the noncompeting model transform into regular solitons, while in the model with the competing nonlinearities they evolve into localized vortical pulsons, which maintain their topological character. Bound states of regular solitons and vortices are constructed too, and their stability is identified.
Description10 pages, 11 figures.-- PACS number(s): 05.45.Yv, 63.20.Ry, 03.75.Lm
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.74.036607
URIhttp://hdl.handle.net/10261/19783
DOI10.1103/PhysRevE.74.036607
ISSN1539-3755
Appears in Collections:(ICMA) Artículos

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