Evolution equation for soft physics at high energy

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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(pp) collisions at high energy. Geometrical scaling occurs at the black disk limit, and scaling develops first for small values of the scaling variable |t|σtot.. Our prediction for d σ/ d t at LHC, with two zeros and a minimum at large |t| differs, as far as we know, from all existing ones.