  On the basis of the representation of the generalized structure of nucleons a
new model of the hadron interaction at high energies is presented. The new
t-dependence of the generalized parton distributions (GPDs) is obtained from
the comparative analysis of different sets of the parton distribution functions
(PDFs), based on the description of the whole sets of experimental data of
electromagnetic form factors of the proton and neutron. Taking into account the
different moments of GPDs of the hadron the quantitative descriptions of all
existing experimental data of the proton-proton and proton-antiproton elastic
scattering from $\sqrt{s} = 9.8$ GeV to $ 8 \ $ TeV, including the Coulomb
range and large momentum transfers up to $-t=15$ GeV$^2$, are obtained with a
few free fitting high energy parameters. The real part of the hadronic elastic
scattering amplitude is determined only through complex $s$ satisfying the
dispersion relations. The negligible contributions of the hard Pomeron and the
presence of the non-small contributions of the maximal Odderon are obtained.
The non-dying form of the spin-flip amplitude is examined as well. The
structure of the Born term and unitarized scattering amplitude are analysed. It
is shown that the Black Disk Limit for the elastic scatering amplitude is not
reached at LHC energies. Predictions for LHC energies are made.
