# Kink-Kink and Kink-Antikink Interactions with Long-Range Tails

Christov, Ivan C. (School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA) ; Decker, Robert J. (Mathematics Department, University of Hartford, West Hartford, Connecticut 06117, USA) ; Demirkaya, A. (Mathematics Department, University of Hartford, West Hartford, Connecticut 06117, USA) ; Gani, Vakhid A. (Department of Mathematics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia) (Theory Department, National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia) ; Kevrekidis, P. G. (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA) ; Khare, Avinash (Physics Department, Savitribai Phule Pune University, Pune 411007, India) ; Saxena, Avadh (Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA)

03 May 2019

Abstract: In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in ${\phi }^{2n+4}$ 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 $2n/\left(n-1\right)$th power of their separation, and we identify the general prefactor for 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 $n=2$ (${\phi }^{8}$ model), $n=3$ (${\phi }^{10}$ model), and $n=4$ (${\phi }^{12}$ model).

Published in: Physical Review Letters 122 (2019)