Radiation-like Shock Waves in Kink Scattering

We study the radiation in kink collision via a model that varies between ${\phi }^6$ theory and ${\phi }^2$ theory with some discontinuities. Both numerical and analytical methods were used to investigate The kink-antikink(KAK) and antikink-kink(AKK) collision. In the numerical analysis, we found the critical velocities in both collisions increased with $n$. We also found a finite lifetime oscillon window in KAK collision for $n=2$. In the analytical part, we found a family of shock wave solutions that describes radiation in the kink collision perfectly. Moreover, an analytical AKK solution at $n\to \mathrm{\infty }$ and $v=1$ was found by considering a certain limit of these solutions.