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We present the complete set of symmetric and antisymmetric (edge and corner)surface modes in finite one-- and two--dimensional arrays of waveguides. Weprovide classification of the modes based on the anti-continuum limit, studytheir stability and bifurcations, and discuss relation between surface and bulkmodes. We put forward existence of surface breathers, which representtwo-frequency modes localized about the array edges.

Surface modes and breathers in finite arrays of nonlinear waveguides