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

Full Abstract

An 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.

Learn Faster Today Improve your study skills

Author information

Author/s: Gómez-Gardeñes, J (J); Malomed, B A (BA); Floría, L M (LM); Bishop, A R (AR);

Affiliation: Departamento de Física de la Materia Condensada and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, E-50009 Zaragoza, Spain.

Journal and publication information

Publication Type: Journal Article

Journal: Physical review. E, Statistical, nonlinear, and soft matter physics (Phys Rev E Stat Nonlin Soft Matter Phys), published in United States. (Language: eng)

Reference: 2006-Sep; vol 74 (issue 3 Pt 2) : pp 036607

Dates: Created 2006/10/09; Completed 2007/01/11;

PMID: 17025764, status: PubMed-not-MEDLINE (last retrieval date: 11/6/2008)

Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.

External Links for this article (including full text providers, if available):

Click Electronic Full-text Provider Links to see options for finding the electronic full text links to this article. Note there may be a subscription or fee required for access to the full text. See our FAQ for information on finding FREE full text articles.

This article may also be located in paper journal collections available in many libraries. Use the Journal and Publication Information above to find the full article.

MeSH headings (categories)

This article was linked to the MESH Headings shown below.

No MeSH Headings found.

The article may not be MeSH Indexed as yet.

These are the highest related articles currently in the database:

See 100+ related articles.