Frequency comb generation for wave transmission through the nonlinear dimer

We study dynamical response of a nonlinear dimer to a symmetrically injected monochromatic wave. We find a domain in the space of frequency and amplitude of the injected wave where all stationary solutions are unstable. In this domain scattered waves carry multiple harmonics with equidistantly spaced frequencies (frequency comb effect). The instability is related to a symmetry protected bound state in the continuum whose response is singular as the amplitude of the injected wave tends to zero.