Radiation-like Shock Waves in Kink Scattering

TL;DR

This paper investigates radiation phenomena in kink collisions across a model interpolating between  and  theories, using numerical and analytical methods to identify critical velocities, oscillon windows, and shock wave solutions.

Contribution

It introduces a family of shock wave solutions for radiation in kink collisions and analytically describes the AKK solution at infinite limit and velocity.

Findings

Critical velocities increase with parameter n.

Finite lifetime oscillon window identified in KAK collision at n=2.

Analytical shock wave solutions accurately describe radiation in kink collisions.

Abstract

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.