  In this work we consider model of asymmetric kinks, where the behavior of the
solution in one side is different from the other side. Also, the models depend
of an integer $n$ and, with the increase of $n$, the constructed kink assumes a
hybrid character: a compactlike profile on one side and a kinklike profile on
the other side. We investigate numerically the kink-antikink and antikink-kink
dynamics, with the aim to understand the effect of the transition of the usual
kink to the semi-compacton structure. The kink-antikink process shows the
formation of one-bounce windows for small values of $n$. The increase of $n$
favors the breaking this structure and the appearance of oscillatory modes. For
antikink-kink collisions we report the appearance of two-bounce windows for
small values of the parameter. We also found an intricate structure of
two-oscillation windows.
