Modified Homotopic Approach For Diffractive Production

We review the recent developments in the use of the homotopy method for solving the non-linear evolution equation for the diffractive production in deep-inelastic scattering. We introduce part of the non-linear corrections in the linear term. This simplified non-linear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. It turns out that these corrections are rather small and can be estimated in the regular iterative procedure.