2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139385We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one-- and two--dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.Accepted for publication in Physical Review EOther Condensed MatterPattern Formation and Solitonstext