= Sine-Gordon multisoliton tau representation
{c}
{title2=$\phi=4\arg(f+ig)$}
For real parameters with $\kappa_i^2-b_i^2=1$, set $E_i=e^{\kappa_i x-b_i t+\gamma_i}$ and $a_{ij}=[(\kappa_i-\kappa_j)^2-(b_i-b_j)^2]/[(\kappa_i+\kappa_j)^2-(b_i+b_j)^2]$. Sum $\prod_i E_i^{\mu_i}\prod_{i<j}a_{ij}^{\mu_i\mu_j}$ over binary vectors of even parity for $f$ and odd parity for $g$. The <Sine-Gordon equation> solution is the continuous field $4\arg(f+ig)$. In the all-<kink> sector, $\kappa_i=\cosh\theta_i$, $b_i=\sinh\theta_i$ and $a_{ij}=-\tanh^2[(\theta_i-\theta_j)/2]$. Treating these coefficients as positive would change the solution. Distinct <rapidities> give separated incoming and outgoing <solitons>.
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