  In this work we investigate several models described by a single real scalar
field with non-polynomial interactions, constructed to support topological
solutions. We do this using the deformation procedure to introduce a function
which allows to construct two distinct families of hyperbolic potentials,
controlled by three distinct parameters, in the standard formalism. In this
way, the procedure allows us to get analytical solutions, and then investigate
the energy density, linear stability and zero mode. We move on and introduce a
non-standard formalism to obtain compact solutions, analytically. We also
investigate these hyperbolic models in the braneworld context, considering both
the standard and non-standard possibilities. The results show how to construct
distinct braneworld models which are implemented via the first order formalism
and are stable against fluctuation of the metric tensor.
