Discrete surface solitons in two dimensions

Details Discrete surface solitons in two dimensions Discrete surface solitons in two dimensions

2006-07-27

arxiv.org/abs/nlin/0607063v1

Phys. Rev. E 75 (2007) 056605

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 4 composite figures

Scientific paper

10.1103/PhysRevE.75.056605

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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