Anderson localization and nonlinearity in flat bands

We explore the interplay between Anderson localization and Kerr nonlinearity in a lattice system containing intersecting flat and dispersive bands. The disordered system supports two distinct types of modes: high energy modes experience conventional Anderson localization. Low energy modes have a much shorter localization length, but are also highly sparse, consisting of multiple, well-separated peaks. Nonlinearity introduces different regimes of wavepacket spreading, determined by which types or modes are strongly coupled together. The spreading of localized excitations can either be massively enhanced, or suppressed, depending on the strength of nonlinearity.