Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays

We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even modes centered at different distances from the surface, and reveal the physical mechanism of the nonlinearity-induced stabilization of surface modes.The authors thank S. Flach for help with the constraint method and acknowledge support from Fondo Nacional de Desarrollo Cientifico y Technólogico grants 1050193 and 7050173 (Chile) and in part from the Australian Research Council