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

TL;DR

This paper derives an explicit formula for the phase shift in ultra-relativistic collisions of non-integrable solitons, applicable to arbitrary periodic potentials, and reveals that kink-kink and kink-antikink collisions share the same leading-order phase shift.

Contribution

It provides the first closed-form expression for phase shifts in high-velocity kink collisions for arbitrary potentials, based on a novel scattering theory using a small kinematic parameter.

Findings

Derived a closed-form phase shift expression for ultra-relativistic kink collisions.

Proved kink-kink and kink-antikink collisions have identical leading-order phase shifts.

Applicable to arbitrary periodic potentials without solving equations of motion.

Abstract

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. Based on our closed-form expression, we prove that kink-kink and kink-antikink collisions have identical phase shifts at leading order.