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In a scalar field theory that has a symmetric octic potential with a quarticminimum and two quadratic minima, kink and mirror kink solutions havelong-range tails. We calculate the force between these kinks when theirlong-range tails overlap. This is a nonlinear problem, solved using anadiabatic ansatz for the accelerating kinks that leads to a modified,first-order Bogomolny equation. We find the force is repulsive and decays withthe fourth power of the kink separation.

Force between Kinks with Long-range Tails