Resonances are signatures of bound states which eventually decay
into the continuum coupled to them. There are many examples of
resonances in different branches of physics, but basically in the
linear quantum systems they are classified as the symmetric
Breit-Wigner or asymmetric Fano resonances. We predict a new type of
resonance in nonlinear systems caused by the interaction of the
transmitted wave with the bound state in the continuum (BSC). Firstly,
the BSC as discrete localized solutions of the single-particle
Schroedinger equation embedded in the continuum of positive energy
states were predicted in 1929 by Neumann and Wigner. For a long time
their analysis was regarded as a mathematical curiosity because of
certain spatially oscillating central symmetric potentials. Later in
1973 the predicted BICs in semiconductor heterostructure superlattices
were observed by Capasso et al as the very narrow absorption peak. In
the last time the phenomenon of BSC was considered in different quantum
and wave propagation systems. In linear systems the BSC displayes
as a collaps of the Fano resonance. In nonlinear systems a direct
coupling of propagating waves with the BSC induces the new
resonance. The width of the new resonance depends on the
nonlinear coefficients and is proportional to the incoming wave. We
demonstrate the BSC induced resonance in the two simplest systems: the
nonlinear two-level Fano-Anderson model and the Fabry-Perot resonator
with nonlinear mirrors.