  In the present work, we adopt a nonlinear scalar field theory coupled to the
gravity sector to model galactic dark matter. We found analytical solutions for
the scalar field coupled to gravity in the Newtonian limit, assuming an
isotropic spacetime and a field potential, with a position dependent form of
the superpotential, which entails the nonlinear dynamics of the model with
self-interactions. The model introduces a position dependent enhancement of the
self-interaction of the scalar fields towards the galaxy center, and while
going towards the galaxy border the interaction tends to vanish building a non
self-interacting DM scenario. The developed approach is able to provide a
reasonable analytical description of the rotation curves in both dwarf and low
surface brightness late-type galaxies, with parameters associated with the
dynamics of the scalar field.
