  In this paper, we investigate novel kinklike structures in a scalar field
theory driven by Dirac-Born-Infeld (DBI) dynamics. Analytical features are
reached through a first-order formalism and a deformation procedure. The
analysis ensures the linear stability of the obtained solutions, and the
deformation method permits to detect new topological solutions given some
systems of known solutions. The proposed models vary according to the
parameters of the theory. However, in a certain parameter regime, their defect
profiles are precisely obtained by standard theories. These are the models
relatives. Besides that, we investigate the $\beta-$Starobinsky potential in
the perspective of topological defects; and we have shown that it can support
kinklike solutions, for both canonical and non-canonical kinetics. As a result,
we propose two new kinds of generalizations on the $\beta-$Starobinsky model,
by considering the DBI approach. Finally, we explore the main characteristics
of such structures in these new scenarios.
