  This work deals with the presence of localized static structures in the real
line, described by relativistic real scalar fields in two spacetime dimensions.
We consider models featuring both standard and modified kinematics, where we
employ two intriguing potentials supporting defect solutions. The first
potential can transform kink into compacton in the standard framework, while
the second one is based on the inflationary Starobinsky model. Interesting
possibilities unseen in previous investigations are described, in particular,
for the case related to the Starobinsky potential. The addressed potentials are
inserted into a broader framework, and so the extended models are described by
a wider set of solutions. This investigation also reveals the presence of the
twinlike behavior for a specific compact configuration, which solves two
distinct models.
