  The distinctive effects of fuzzy dark matter are most visible at non-linear
galactic scales. We present the first simulations of mixed fuzzy and cold dark
matter, obtained with an extended version of the Nyx code. Fuzzy (or
ultralight, or axion-like) dark matter dynamics are governed by the comoving
Schr\"odinger-Poisson equation. This is evolved with a pseudospectral algorithm
on the root grid, and with finite differencing at up to six levels of adaptive
refinement. Cold dark matter is evolved with the existing N-body implementation
in Nyx. We present the first investigations of spherical collapse in mixed dark
matter models, focusing on radial density profiles, velocity spectra and
soliton formation in collapsed halos. We find that the effective granule masses
decrease in proportion to the fraction of fuzzy dark matter which quadratically
suppresses soliton growth, and that a central soliton only forms if the fuzzy
dark matter fraction is greater than 10\%. The Nyx framework supports baryonic
physics and key astrophysical processes such as star formation. Consequently,
AxioNyx will enable increasingly realistic studies of fuzzy dark matter
astrophysics.
