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 \(n\rightarrow\infty\) and \(v=1\) was found by considering a certain limit of these solutions.