  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.
