Discrete surface solitons in two dimensions

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, D. J. Frantzeskakis

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageBritish English
Article number056605
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - 9 May 2007


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