  This paper presents the first numerical solution to the non-linear evolution
equation for diffractive dissociation processes in deep inelastic scattering.
It is shown that the solution depends on one scaling variable $\tau = Q^2/Q^{D
2}_s(x,x_0)$, where $Q^D_s(x,x_0)$ is the saturation scale for the diffraction
processes. The dependence of the saturation scale $Q^D_s(x,x_0)$ on both $x$
and $x_0$ is investigated, ($Y_0 = \ln(1/x_0)$ is a minimal rapidity gap for
the diffraction process). The $x$ - dependence of $Q^D_s$ turns out to be the
same as of the saturation scale in the total inclusive DIS cross section. In
our calculations $Q^D_s(x,x_0)$ reveals only mild dependence on $x_0$. The
scaling is shown to hold for $x \ll x_0$ but is violated at $ x \sim x_0$.
