Transmission of nonlinear localized modes through waveguide bends

In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes of the interaction of a moving pulse with the bend, as a function of the bend’s strength and the initial velocity of the pulse. Comparisons with the linear counterpart of the model are also discussed. Some features, such as transition from capture to reflection, may be explained by an analytical perturbation theory based on the quasi-continuum approximation.