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

Semi-compactness and multiple oscillating pulses in kink scattering