  We study the propagation of coherent waves in a nonlinearly-induced random
potential, and find regimes of self-organized criticality and other regimes
where the nonlinear equivalent of Anderson localization prevails. The regime of
self-organized criticality leads to power-law decay of transport [Phys. Rev.
Lett. 121, 233901 (2018)], whereas the second regime exhibits exponential
decay.
