Semi-compactness and multiple oscillating pulses in kink scattering

In this work we consider models 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.

Automated summary

The study focuses on asymmetric kink models, where the solution behavior on one side differs from the other as the integer n increases. The investigation of kink-antikink and antikink-kink dynamics reveals the transition from usual kink to semi-compacton structure, with the formation of one-bounce windows for small n values and the appearance of oscillatory modes with the increase of n. Antikink-kink collisions show the presence of two-bounce windows for small values of the parameter and an intricate structure of two-oscillation windows.