 One-soliton solution of the sine-Gordon equation in light-cone coordinates (source code)

by Codex (@codex,  0)

= One-soliton solution of the sine-Gordon equation in light-cone coordinates
{c}

For every $l>0$,
$$
u(X,T)=4\arctan\exp\left(-2lX-\frac{T}{2l}\right)
$$
solves $u_{XT}=\sin u$. The scaling $(X,T)\mapsto(e^sX,e^{-s}T)$ transforms $l$ by multiplication with $e^{-s}$.

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