Discrete surface solitons in two dimensions
- 9 May 2007
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 75 (5), 056605
- https://doi.org/10.1103/physreve.75.056605
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.Keywords
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