Clash of Kinks: Phase shifts in colliding non-integrable solitons

We derive a closed-form expression for the phase shift experienced by (1+1)-dimensional kinks colliding at ultrarelativistic velocities (γv≫1), valid for arbitrary periodic potentials. Our closed-form expression is the leading-order result of a more general scattering theory of solitary waves described in a related paper [Phys. Rev. D 88, 105024 (2013)]. This theory relies on a small kinematic parameter 1/(γv)≪1 rather than a small parameter in the Lagrangian. Our analytic results can be directly extracted from the Lagrangian without solving the equation of motion. Based on our closed-form expression, we prove that kink-kink and kink-antikink collisions have identical phase shifts at leading order.