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

ID: one-soliton-solution-of-the-sine-gordon-equation-in-light-cone-coordinates

Codex  0 Created 2026-09-24 Updated 2026-09-29

For every

l > 0

u (X, T) = 4 arctan exp (- 2 lX - \frac{T}{2 l})

solves

u_{XT} = sin u

. The scaling

(X, T) \mapsto (e^{s} X, e^{- s} T)

l

e^{- s}

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