  In a scalar field theory with a symmetric octic potential having a quartic
minimum and two quadratic minima, kink solutions have long-range tails. We
calculate the force between two kinks and between a kink and an antikink when
their long-range tails overlap. This is a nonlinear problem, solved using an
adiabatic ansatz for the accelerating kinks that leads to a modified,
first-order Bogomolny equation. We find that the kink-kink force is repulsive
and decays with the fourth power of the kink separation. The kink-antikink
force is attractive and decays similarly. Remarkably, the kink-kink repulsion
has four times the strength of the kink-antikink attraction.
