Mustafa A. Amin, Eugene A. Lim, I-Sheng Yang
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 (2013)]. 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. Based on our closed-form expression, we prove that kink-kink and kink-antikink collisions have identical phase shifts at leading order.
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http://arxiv.org/abs/1308.0605
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