Abstract
A model equation governing the amplitude of the electric field in an array of coupled optical waveguides embedded in a material with Kerr nonlinearities is derived and explored. The equation is an extended discrete nonlinear Schrödinger equation with intersite nonlinearities. Attention is turned towards localized solutions and investigations are made from the viewpoint of the theory of discrete breathers (DBs). Stability analysis reveals an inversion of stability between stationary one-site and symmetric or antisymmetric two-site solutions connected to bifurcations with a pair of asymmetric intermediate DBs. The stability inversion leads to the existence of high-intensity narrow mobile solutions, which can propagate essentially radiationless. The direction and transverse velocity of the mobile solutions can be controlled by appropriate perturbations. Such solutions may have an important application for multiport switching, allowing unambiguous selection of output channel. The derived equation also supports compact DBs, which in some sense yield the best possible solutions for switching purposes.
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