  We investigate braneworlds modeled by topological solutions that arise from
the so-called Cuscuta-Galileon model. We develop a first order framework and
illustrate our procedure with the scalar field having the well-known hyperbolic
tangent profile. We find conditions that must be imposed to the parameters of
the model in order to have solutions connecting minima of the potential, with
the brane constrained to interpolate Minkowski and anti de Sitter geometries.
We also find solutions where the brane only interpolates anti de Sitter
geometry. In both cases, the gravity sector of the brane is stable against
small fluctuations of the metric.
