  We study excitation of gap solitons under the conditions of coherent perfect
absorption (CPA). Our system consists of a symmetric periodic structure with
alternating Kerr nonlinear and linear layers, illuminated from both the ends.
We show near-total transfer of incident light energy into the gap solitons
resulting in null-scattering. We also report on the nonlinear super-scattering
(SS) states. Both the CPA and the SS states are shown to be characterized by
typical field distributions. Both the exact and the approximate results (based
on nonlinear characteristic matrix method) are presented, which show good
agreement.
