= Bianchi permutability for sine-Gordon Bäcklund transformations
{c}
{title2=$\tan[(u_{ab}-u_0)/4]=\frac{a+b}{b-a}\tan[(u_b-u_a)/4]$}
= Sine-Gordon superposition formula
{c}
{synonym}
Two compatible Bäcklund steps commute after integration constants are matched. The displayed superposition relation constructs their common output algebraically from the seed and the two one-step outputs, in the reciprocal-parameter convention of the <Sine-Gordon Bäcklund transformation>. It uses the angular field $u=\beta\phi$. Smooth inverse-tangent branch continuation is required to retain the correct vacuum labels.
Back to article page
