= Sine-Gordon two-kink time advance
{c}
{title2=$\Delta t=2\log v/(m\gamma v)<0$}
For two equal-charge <Sine-Gordon kinks> with speeds $\pm v$, $0<v<1$, the positive spatial transition satisfies $X_+(T)=v|T|-\log v/(m\gamma)+o(1)$, where $\gamma=(1-v^2)^{-1/2}$. Labeling a <soliton> by its preserved <rapidity>, the right-moving incoming and outgoing intercepts differ by $-2\log v/(m\gamma)$. The <soliton time delay> at a fixed distant location is minus this shift divided by $v$, giving the displayed negative value. Reversing the entire field gives two <antikinks> with the same shifts. The sign means an advance relative to extrapolation of the incoming line; labels tied to left and right positions instead exchange <velocities> during reflection.
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