= Pairwise additivity of soliton shifts
{title2=$\Delta x_i=\sum_{j\ne i}\Delta x_{i|j}$}
A many-<soliton> spatial shift is pairwise additive when $\Delta x_i=\sum_{j\ne i}\Delta x_{i|j}$. In the all-<kink> sector of <Sine-Gordon theory>, $\Delta x_{i|j}=-\operatorname{sgn}(v_i-v_j)\log\tanh^2[(\theta_i-\theta_j)/2]/\cosh\theta_i$. Dominant spectator exponentials in the <Sine-Gordon multisoliton tau representation> multiply the effective exponential of <kink> $i$, so their logarithms add. This is a classical signature of <factorized scattering>, with no independent many-body contribution to the asymptotic shift.
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