  Coherent perfect absorption is the complete extinction of incoming radiation
by a complex potential in a physical system supporting wave propagation. The
concept was proven for linear waves in variety of systems including light
interacting with absorbing scatterers, plasmonic metasurfaces and graphene
films, as well as sound waves. We extend the paradigm to coherent perfect
absorption of nonlinear waves and experimentally demonstrate it for matter
waves in an atomic Bose-Einstein condensate. Coherent absorption of nonlinear
matter waves is achieved easier than its linear analogs because the strength of
two-body interactions offers additional freedom for control. Implementation of
the coherent perfect absorber of Bose-Einstein condensates paves the way
towards broad exploitation of the phenomenon in nonlinear optics,
exciton-polariton condensates, acoustics, and other areas of nonlinear physics.
It also opens perspectives for designing atomic laser.
