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arXiv · 1811.07872

Kink-kink and kink-antikink interactions with long-range tails

Ivan C. Christov·Robert J. Decker·A. Demirkaya·Vakhid A. Gani·P. G. Kevrekidis·Avinash Khare·Avadh Saxena
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Abstract

In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $φ^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of $n=2$ ($φ^8$ model), $n=3$ ($φ^{10}$ model) and $n=4$ ($φ^{12}$ model).

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Ivan C. Christov, Robert J. Decker, A. Demirkaya, Vakhid A. Gani, P. G. Kevrekidis, Avinash Khare, Avadh Saxena. 2019-03-29. Kink-kink and kink-antikink interactions with long-range tails. https://doi.org/10.1103/physrevlett.122.171601

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