  In this paper we solved the new evolution equation for high energy scattering
amplitudethat stems from the Gribov-Zwanziger approach to the confinement of
quarks and gluons. We found that (1) the energy dependence of the scattering
amplitude turns out to be the same as for QCD BFKL evolution; (2) the spectrum
of the new equation does not depend on the details of the Gribov-Zwanzinger
approach and (3) all eigenfunctions coincide with the eigenfunctions of the QCD
BFKL equation at large transverse momenta $\kappa\,\geq\,1$. The numerical
calculations show that there exist no new eigenvalues with the eigenfunctions
which decrease faster than solutions of the QCD BFKL equation at large
transverse momenta. The structure of the gluon propagator in Gribov-Zwanziger
approach, that stems from the lattice QCD and from the theoretical evaluation,
results in the exponential suppression of the eigenfunctions at long distances
and in the resolution of the difficulties, which the Colour Glass Condensate
(CGC) and some other approaches, based on perturbative QCD, face at large
impact parameters. We can conclude that the confinement of quark and gluons, at
least in the form of Gribov-Zwanziger approach, does not influence on the
scattering amplitude except solving the long standing theoretical problem of
its behaviour at large impact parameters.
