= Sine-Gordon kink-antikink scattering solution
{c}
{title2=$u=-4\arctan[\sinh(m\Gamma vt)/(v\cosh(m\Gamma x))]$}
This localized two-soliton field has zero net winding and describes an elastic kink-antikink collision for $0<v<1$. Two reciprocal positive Bäcklund parameters produce it from the vacuum. Analytic continuation of $v$ to an imaginary value gives a real <Sine-Gordon breather>. The overall field sign and spacetime translations change conventions, not the field equation.
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