  We develop a Coherent Perfect Absorption (CPA) protocol for cases where scale
invariance is violated due to the presence of nonlinear mechanisms. We
demonstrate, using a microwave setting that lacks geometrical symmetries, that
the nonlinearity offers new reconfigurable modalities: the destruction or
formation of nonlinear CPAs (NL-CPAs), and their frequency positioning and
bandwidth management using the incident power as a control knob. The latter
occurs via the formation of exceptional point degeneracies of the zeroes of
nonlinear scattering processes. Our results establish NL-CPA protocols as a
versatile scheme for the creation of reconfigurable hot/cold-spots in
complicated enclosures (e.g. buildings or vessels) with applications to
next-generation telecommunications, long-range wireless power transfer, and
electromagnetic warfare.
