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

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 Φ^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 Φ^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,ω) 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 Φ^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.

arXiv comment8 pages, 9 figures. The Mathematica files used for the production of the figures may be downloaded from http://leandros.physics.uoi.gr/partkinks.zip

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• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• An introduction to kinks in ${\phi }^4$-theory
• Emergence of oscillons in kink-impurity interactions
• Vacuum state perturbed by an oscillon: composite configurations in ${\varphi }^4$ model