  Wave Dark Matter (WaveDM) has recently gained attention as a viable candidate
to account for the dark matter content of the Universe. In this paper we
explore the extent to which dark matter halos in this model, and under what
conditions, are able to reproduce strong lensing systems. First, we
analytically explore the lensing properties of the model -- finding that a pure
WaveDM density profile, a soliton profile, produces a weaker lensing effect
than other similar cored profiles. Then we analyze models with a soliton
embedded in an NFW profile, as has been found in numerical simulations of
structure formation. We use a benchmark model with a boson mass of
$m_a=10^{-22}{\rm eV}$, for which we see that there is a bi-modality in the
contribution of the external NFW part of the profile, and actually some of the
free parameters associated with it are not well constrained. We find that for
configurations with boson masses $10^{-23}$ -- $10^{-22}{\rm eV}$, a range of
masses preferred by dwarf galaxy kinematics, the soliton profile alone can fit
the data but its size is incompatible with the luminous extent of the lens
galaxies. Likewise, boson masses of the order of $10^{-21}{\rm eV}$, which
would be consistent with Lyman-$\alpha$ constraints and consist of more compact
soliton configurations, necessarily require the NFW part in order to reproduce
the observed Einstein radii. We then conclude that lens systems impose a
conservative lower bound $m_a > 10^{-24}$ and that the NFW envelope around the
soliton must be present to satisfy the observational requirements.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology