A scattering theory of ultrarelativistic solitons
  We construct a perturbative framework for understanding the collision of
solitons (more precisely, solitary waves) in relativistic scalar field
theories. Our perturbative framework is based on the suppression of the
space-time interaction area proportional to $1/(\gamma v)$, where $v$ is the
relative velocity of an incoming solitary wave and $\gamma = 1/\sqrt{1-v^2} \gg
1$. We calculate the leading order results for collisions of (1+1) dimensional
kinks in periodic potentials, and provide explicit, closed form expressions for
the phase shift and the velocity change after the collisions. We find excellent
agreement between our results and detailed numerical simulations. Crucially,
our perturbation series is controlled by a kinematic parameter, and hence not
restricted to small deviations around integrable cases such as the Sine-Gordon
model.
