### abstract

- 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 \(\tau = Q^2/Q^{\mathrm{{D 2}}}_{\mathrm{s}}(x,x_0)\), where \(Q^{\mathrm{D}}_{\mathrm{s}}(x,x_0)\) is the saturation scale for the diffraction processes. The dependence of the saturation scale \(Q^{\mathrm{D}}_{\mathrm{s}}(x,x_0)\) on both x and \(x_0\) is investigated, (\(Y_0 = \ln(1/x_0)\) is the minimal rapidity gap for the diffraction process). The x-dependence of \(Q^{\mathrm{D}}_{\mathrm{s}}\) turns out to be the same as the one of the saturation scale in the total inclusive DIS cross section. In our calculations \(Q^{\mathrm{D}}_{\mathrm{s}}(x,x_0)\) reveals only a mild dependence on \(x_0\). The scaling is shown to hold for \(x \ll x_0\) but is violated at \( x \sim x_0\).