Kink-Antikink Formation from an Oscillation Mode by Sudden Distortion of the Evolution Potential

TL;DR

This paper numerically demonstrates that oscillation modes like breathers or oscillons in 1+1 dimensions can decay into kink-antikink pairs when the potential is suddenly distorted, revealing a new mechanism for soliton formation.

Contribution

It introduces a novel mechanism for kink-antikink formation via sudden potential changes, applicable to breathers and oscillons, with implications for higher dimensions.

Findings

Kink-antikink pairs form when breather energy exceeds pair energy in the new potential.

Sudden potential distortion can induce soliton formation from oscillation modes.

The mechanism applies to both sine-Gordon to  potential transitions and oscillons.

Abstract

We demonstrate numerically that an oscillation mode in 1+1 dimensions (eg a breather or an oscillon) can decay into a kink-antikink pair by a sudden distortion of the evolution potential which occurs within a certain time or space domain. In particular, we consider the transition of a sine-Gordon potential into a \Phi^4 potential. The breather field configuration is assumed to initially evolve in a sine-Gordon potential with velocity $v$ and oscillation frequency $\omega$. We then consider two types of numerical experiments: a. An abrupt transition of the potential to a $\Phi^4$ form at t_0=0 over the whole 1-dimensional lattice and b. The impact of the breather on a region x>x_0=0 where the potential has the \Phi^4 form which is different from the sine-Gordon form valid at x<x_0=0. We find that in both cases there is a region of parameters (v,\omega) such that the breather decays to a kink-antikink pair. This region of parameters for kink-antikink formation is qualitatively similar with the parameter region where the energy of the breather exceeds the energy of the kink-antikink pair in the \Phi^4 potential. We demonstrate that the same mechanism for soliton formation is realized when using a gaussian oscillator (oscillon) instead of a breather. We briefly discuss the implications of our results for realistic experiments as well as their extension to soliton formation in two and three space dimensions.