  In a scalar field theory that has a symmetric octic potential with a quartic
minimum and two quadratic minima, kink and mirror kink solutions have
long-range tails. We calculate the force between these kinks 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 the force is repulsive and decays with
the fourth power of the kink separation.
