 Periodic backward-sawtooth Burgers solution

For the negative-flux equation $f_Z-f{f}_{\theta }=0$, a period-two increasing initial ramp develops rarefaction fans at odd points and steepens at even points. Before $Z=1$, its central ramp is $f=(\theta -2m)/(1-Z)$ on $|\theta -2m|<1-Z$, and its odd-point fans are $f=-(\theta -(2m+1))/Z$. After $Z=1$, stationary compressive shocks occupy the even points and $f=(2m+1-\theta )/Z$ between consecutive shocks. The amplitude decays as $1/Z$. The Rankine-Hugoniot condition and incoming characteristic speeds certify the post-breaking entropy solution.