Publication Date

2007

Journal or Book Title

Physics Review E

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.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v75/i5/e056605

Volume

75

Issue

5

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