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Discrete surface solitons in two dimensions

H. Susanto·P. G. Kevrekidis·B. A. Malomed·R. Carretero-Gonzalez·D. J. Frantzeskakis
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Abstract

We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the contrary, lattice vortices cannot exist too close to the border. Furthermore, we show analytically and numerically that the edge stabilizes a novel wave species, which is entirely unstable in the uniform lattice, namely, a "horseshoe" soliton, consisting of 3 sites. Unstable horseshoes transform themselves into a pair of ordinary solitons.

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H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, D. J. Frantzeskakis. 2006-07-27. Discrete surface solitons in two dimensions. https://doi.org/10.1103/physreve.75.056605

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