Nonlinear Fano resonance and bistable wave transmission

We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar Fano-Anderson model, and it can generate the amplitude depended bistable resonant transmission or reflection. We identify these effects as the nonlinear Fano resonance, and study its properties for continuous waves and pulses.