  Based on the non-linear logistic equation we study, in a qualitative and
semi-quantitative way, the evolution with energy and saturation of the elastic
differential cross-section in $pp(\bar{p}p)$ collisions at high energy.
Geometrical scaling occurs at the black disk limit, and scaling develops first
for small values of the scaling variable $|t|\sigma_{tot.}$. Our prediction for
$d \sigma / \ d t$ at LHC, with two zeros and a minimum at large $|t|$ differs,
as far as we know, from all existing ones.
