= Midpoint symmetry of a viscous Burgers step
{title2=$f(z,-Uz-\theta)=U-f(z,\theta)$}
The <viscous Burgers step solution with negative flux> is symmetric around $\theta=-Uz/2$ after subtracting $U/2$. Its Gaussian-tail ratio equals one precisely at this midpoint, giving $f=U/2$ for either sign of $U$. For $U>0$ this point becomes the entropy-shock center in the <vanishing viscosity approximation>; for $U<0$ it is the center of a <rarefaction wave>. The same trajectory therefore does not by itself identify a <shock>.
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