Discrete surface solitons in two dimensions

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis
Phys. Rev. E 75, 056605 – Published 9 May 2007

Abstract

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 26 July 2006

DOI:https://doi.org/10.1103/PhysRevE.75.056605

©2007 American Physical Society

Authors & Affiliations

H. Susanto1, P. G. Kevrekidis1, B. A. Malomed2, R. Carretero-González3, and D. J. Frantzeskakis4

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
  • 2Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
  • 3Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California, 92182-7720, USA
  • 4Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 75, Iss. 5 — May 2007

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×