  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.
