Evolution equation for elastic scattering of hadrons

We turn high energy elastic scattering of hadrons into an initial value problem using evolution equation based on the Regge Field Theory, which has a form complex nonlinear reaction-diffusion equation, with time being played by logarithm energy. The conditions are provided data-driven models for real and imaginary parts amplitude. Numerical calculations pp differential cross sections forward quantities LHC energies agree very well experimental data extending up to, including diffractive cone. Furthermore, we show that at current accessible non-linear effects play important role, as impact parameter space profiles approach unitarity bound. also predicts some other discussed in literature, like hollowness nuclear matter or existence stationary points momentum transfer t.