= Solution
Put $u=t-z$. Wherever $|u|>U$, the profile $A(u)$ vanishes and the displayed metric is exactly the <Minkowski metric>. Thus the two flat regions in the $(t,z)$-plane are the half-planes $t-z>U$ and $t-z<-U$, separated by the strip
$$
\boxed{|t-z|\leq U}.
$$
At fixed $t$ this strip is $t-U\leq z\leq t+U$, so it has longitudinal width $2U$. A surface $u=\text{constant}$ obeys $z=t-u$ and travels in the positive $z$ direction at the <speed of light>. The curvature is confined to that moving strip, identifying the solution as a <gravitational-wave pulse> represented by a <plane-fronted gravitational wave>.
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