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

Understand

We derive a closed-form expression for the phase shift experienced by 1+1 dimensional kinks colliding at ultra-relativistic velocities (gamma v >> 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 companion paper [Amin, Lim and Yang, arXiv:1308.0606].
• This theory relies on a small kinematic parameter 1/(gamma v) << 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.