  The era of precision cosmology allows us to test the composition of the dark
matter. Mixed ultralight or fuzzy dark matter (FDM) is a cosmological model
with dark matter composed of a combination of particles of mass $m\leq
10^{-20}\;\mathrm{eV}$, with an astrophysical de Broglie wavelength, and
particles with a negligible wavelength sharing the properties of cold dark
matter (CDM). In this work, we simulate cosmological volumes with a dark matter
wave function for the ultralight component coupled gravitationally to CDM
particles. We investigate the impact of a mixture of CDM and FDM in various
proportions $(0\%,\;1\%,\;10\%,\;50\%,\;100\%)$ and for ultralight particle
masses ranging over five orders of magnitude $(2.5\times
10^{-25}\;\mathrm{eV}-2.5\times 10^{-21}\;\mathrm{eV})$. To track the evolution
of density perturbations in the non-linear regime, we adapt the simulation code
AxioNyx to solve the CDM dynamics coupled to a FDM wave function obeying the
Schr\"odinger-Poisson equations. We obtain the non-linear power spectrum and
study the impact of the wave effects on the growth of structure on different
scales. We confirm that the steady-state solution of the Schr\"odinger-Poisson
system holds at the center of halos in the presence of a CDM component when it
composes $50\%$ or less of the dark matter but find no stable density core when
the FDM accounts for $10\%$ or less of the dark matter. We implement a modified
friends-of-friends halo finder and find good agreement between the observed
halo abundance and the predictions from the adapted halo model axionHMCode.
