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Sine-Gordon equation

{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 $e^{-s}$.


One-soliton solution of the sine-Gordon equation in light-cone coordinates

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 34E / Solution

One-soliton solution of the sine-Gordon equation in light-cone coordinates

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One-soliton solution of the sine-Gordon equation in light-cone coordinates

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