High energy density spots and production of kink-antikink pairs in particle collisions

TL;DR

This paper numerically investigates the maximum energy density in wave train collisions within the $^4$ model, predicting kink-antikink pair production based on energy density limits, and confirms these predictions with simulation results.

Contribution

It introduces a numerical approach to predict kink-antikink pair production from energy density in wave train collisions, aligning predictions with simulation data.

Findings

Maximal energy density in wave train collisions is characterized.

Number of kink-antikink pairs correlates with energy density predictions.

Numerical results agree with theoretical predictions.

Abstract

The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the $\phi^4$ model has been investigated numerically for different wave train parameters. From these results the prediction is made on how many kink-antikink pairs can be produced in wave train collisions taking into account that in collision of $N$ kinks maximal energy density is equal to $N^2/2$ for even $N$. Our numerical results are in a reasonably good agreement with the predicted maximal number of kink-antikink pairs formed in wave train collisions.