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Phys. Rev. E 78, 036605 (2008) [10 pages]

Surface solitons in three dimensions

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Q. E. Hoq1, R. Carretero-González2, P. G. Kevrekidis3, B. A. Malomed4, D. J. Frantzeskakis5, Yu. V. Bludov6, and V. V. Konotop6,7
1Department of Mathematics, Western New England College, Springfield, Massachusetts 01119, USA
2Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720, USA
3Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
4Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
5Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84, Greece
6Centro de Física Teórica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal
7Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Piso 6, Lisboa 1749-016, Portugal

Received 5 June 2008; published 17 September 2008

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site “horseshoe”-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anticontinuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface, the increased stability-region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.78.036605
DOI:
10.1103/PhysRevE.78.036605
PACS:
05.45.Yv
 
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