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

In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ²ⁿ⁺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/(n-1)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 (φ⁸ model), n=3 (φ¹⁰ model), and n=4 (φ¹² model).