= Sine-Gordon two-kink solution
{c}
{title2=$u=4\arctan[v\sinh(m\Gamma x)/\cosh(m\Gamma vt)]$}
For $0<v<1$ and $\Gamma=(1-v^2)^{-1/2}$, this real two-soliton solution has angular winding $4\pi$. Its separated <kink> velocities are $\pm v$. At large times the centers satisfy $|m\Gamma x|=|m\Gamma vt|-\log v+o(1)$, giving a right-moving shift $-2\log v/(m\Gamma)$. It follows from <Bianchi permutability for sine-Gordon Bäcklund transformations> with oppositely signed seed parameters.
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