Discrete surface solitons in two dimensions

被引:32
作者
Susanto, H. [1 ]
Kevrekidis, P. G.
Carretero-Gonzalez, B. A. Malomed R.
Frantzeskakis, D. J.
机构
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[2] Tel Aviv Univ, Fac Engn, Sch Elect Engn, Dept Interdisciplinary Studies, IL-69978 Tel Aviv, Israel
[3] San Diego State Univ, Dept Math & Stat, Nonlinear Dynam Syst Grp, San Diego, CA 92182 USA
[4] San Diego State Univ, Computat Sci Res Ctr, San Diego, CA 92182 USA
[5] Univ Athens, Dept Phys, GR-15784 Athens, Greece
来源
PHYSICAL REVIEW E | 2007年 / 75卷 / 05期
关键词
D O I
10.1103/PhysRevE.75.056605
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We investigate fundamental localized modes in two-dimensional lattices with an edge (surface). The interaction with the edge expands the stability area for fundamental solitons, and induces a difference between dipoles oriented perpendicular and parallel to the surface. On the contrary, lattice vortex solitons cannot exist too close to the border. We also show, analytically and numerically, that the edge supports a species of localized patterns, which exists too but is unstable in the uniform lattice, namely, a horseshoe-shaped soliton, whose "skeleton" consists of three lattice sites. Unstable horseshoes transform themselves into a pair of ordinary solitons.
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页数:8
相关论文
共 37 条
[1]   Wannier functions analysis of the nonlinear Schrodinger equation with a periodic potential [J].
Alfimov, GL ;
Kevrekidis, PG ;
Konotop, VV ;
Salerno, M .
PHYSICAL REVIEW E, 2002, 66 (04) :6
[2]   Three-dimensional nonlinear lattices:: From oblique vortices and octupoles to discrete diamonds and vortex cubes -: art. no. 203901 [J].
Carretero-González, R ;
Kevrekidis, PG ;
Malomed, BA ;
Frantzeskakis, DJ .
PHYSICAL REVIEW LETTERS, 2005, 94 (20)
[3]   Surface defect gap solitons [J].
Chen, W. H. ;
He, Y. J. ;
Wang, H. Z. .
OPTICS EXPRESS, 2006, 14 (23) :11271-11276
[4]   Formation of discrete solitons in light-induced photonic lattices [J].
Chen, ZG ;
Martin, H ;
Eugenieva, ED ;
Xu, JJ ;
Yang, JK .
OPTICS EXPRESS, 2005, 13 (06) :1816-1826
[5]  
Dodd R. K., 1982, Solitons and nonlinear wave equations
[6]   Observation of vortex-ring "discrete" solitons in 2D photonic lattices [J].
Fleischer, JW ;
Bartal, G ;
Cohen, O ;
Manela, O ;
Segev, M ;
Hudock, J ;
Christodoulides, DN .
PHYSICAL REVIEW LETTERS, 2004, 92 (12) :123904-1
[7]   Surface multi-gap vector solitons [J].
Garanovich, Ivan L. ;
Sukhorukov, Andrey A. ;
Kivshar, Yuri S. ;
Molina, Mario .
OPTICS EXPRESS, 2006, 14 (11) :4780-4785
[8]   Growth and decay of discrete nonlinear Schrodinger breathers interacting with internal modes or standing-wave phonons [J].
Johansson, M ;
Aubry, S .
PHYSICAL REVIEW E, 2000, 61 (05) :5864-5879
[9]   Surface vortex solitons [J].
Kartashov, YV ;
Egorov, AA ;
Vysloukh, VA ;
Torner, L .
OPTICS EXPRESS, 2006, 14 (09) :4049-4057
[10]   Surface gap solitons [J].
Kartashov, YV ;
Vysloukh, VA ;
Torner, L .
PHYSICAL REVIEW LETTERS, 2006, 96 (07)