= Power-law river kinematic wave
{title2=$A_t+[cA^{m+1}/(m+1)]_s=M$}
With constant lateral supply $M$, a discharge law of the displayed form gives <equilibrium> <area> $[(m+1)(Q_{\rm in}+Ms)/c]^{1/(m+1)}$ and <characteristic> <speed> $cA^m$. Under a <Chézy friction law>[Chezy law], a wetted-perimeter relation $P_b\propto A^q$ gives $m=(1-q)/2$. Small <area> perturbations are transported downstream with <amplitude> inversely proportional to this <characteristic> <speed>; finite compressive disturbances can still form shocks because the <flux> is <convex>.
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