  The topological structures that arise from two-dimensional models are
relevant physically and the first step towards understanding more complex
systems. In this work, one studies the kink-like solutions of the matter field
that emerge in a two-dimensional dilaton gravity scenario. Considering this
scenario, we examine the linear stability of the matter field and the
translational mode. Due to the specific profile of the solutions found, a
differential configurational complexity (DCC) analysis of the system was
necessary to confirm the nature of the structures. Furthermore, we study the
interforce and scattering process, considering a pair of kink-antikink-like
solutions in a fixed time ($t=0$).
