We study interactions of kinks and antikinks of the (1 + 1)-dimensional ϕ 8 model. In this model, there are kinks with mixed tail asymptotics: power-law behavior at one infinity versus exponential decay towards the other. We show that if a kink and an antikink face each other in way such that their power-law tails determine the kink-antikink interaction, then the force of their interaction decays slowly, as some negative power of distance between them. We estimate the force numerically using the collective coordinate approximation, and analytically via Manton's method (making use of formulas derived for the kink and antikink tail asymptotics).

We study excitations of solitary waves -the kinks -in scalar models with degree eight polynomial self-interaction in (1 + 1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other and analyse the occurring resonance phenomena. We connect these phenomena to the energy exchange between the translational and the vibrational modes of the colliding kinks. We also point out that the interaction of two kinks with power-law asymptotic can lead to a long-range interaction between the two kinks.