= Extremal-state asymptotics of exponential Burgers solutions
{title2=$s=-(q_1+q_N)/2$}
For ordered states $q_1<\cdots<q_N$, in the moving frame $\theta=sZ+\xi$ the first and last exponents in the <finite-exponential Cole-Hopf solution> have the same leading coefficient. Each interior state's coefficient is smaller by $(q_j-q_1)(q_N-q_j)/(4\epsilon)>0$. Thus the large-$Z$ moving-frame profile is the two-state shock between the extremes. At fixed $\theta$, the endpoint of largest absolute value dominates; equal opposite extremes leave a stationary shock.
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