  We experimentally and theoretically challenge the concept of coherent perfect
absorption (CPA) as a narrow frequency resonant mechanism associated with
scattering processes that respect scale-invariance. Using a microwave platform,
consisting of a lossy nonlinear resonator coupled to two interrogating
antennas, we show that a coherent incident excitation can trigger a
self-induced perfect absorption once its intensity exceeds a critical value.
Importantly, a (near) perfect absorption persists for a broad band frequency
range around the nonlinear CPA condition. Its origin is traced to a quartic
behavior that the absorbance spectrum acquires in the proximity of a CPA
associated with a new kind of exceptional point degeneracy related to the zeros
of the nonlinear scattering operator.
