  In this paper we derive the high energy evolution equation in the
Gribov-Zwanziger approach, for the confinement of quarks and gluons. We
demonstrate that the new equation generates an exponential decrease of the
scattering amplitude at large impact parameter, and resolves the main
difficulties of CGC (Colour Glass Condensate) high energy effective theory.
Such behaviour occurs if the gluon propagator in Gribov-Zwanziger approach,
does not vanish at small momenta. Solving the non-linear equation for deep
inelastic scattering, we show that the suggested equation leads to a Froissart
disc with radius ($R_F$), which increases as $ R_F \,\propto Y = \ln (1/x)$,
and with a finite width for the distribution over $| b - R_F|$.
