  Analytic arguments and numerical simulations show that bosonic ultra-light
dark matter (ULDM) would form cored density distributions (`solitons') at the
center of galaxies. ULDM solitons offer a promising way to exclude or detect
ULDM by looking for a distinctive feature in the central region of galactic
rotation curves. Baryonic contributions to the gravitational potential pose an
obstacle to such analyses, being (i) dynamically important in the inner galaxy
and (ii) highly non-spherical in rotation-supported galaxies, resulting in
non-spherical solitons. We present an algorithm for finding the ground state
soliton solution in the presence of stationary non-spherical background
baryonic mass distribution. We quantify the impact of baryons on the predicted
ULDM soliton in the Milky Way and in low surface-brightness galaxies from the
SPARC database.
