Modified homotopy approach for diffractive production in the saturation region

TL;DR

This paper develops a modified homotopy method to analytically solve a simplified nonlinear evolution equation for diffractive production in deep inelastic scattering, demonstrating the smallness of nonlinear corrections and their iterative estimation.

Contribution

It introduces a novel homotopy-based approach to solve nonlinear evolution equations in diffractive scattering, including perturbative correction estimation.

Findings

Analytical solution for simplified nonlinear evolution equation.

Small nonlinear corrections estimated via iterative procedure.

Perturbative method applicable to remaining nonlinear parts.

Abstract

In this paper we continue to develop the homotopy method for solving of the non linear evolution equation for the diffractive production in deep inelastic scattering(DIS). We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the non-linear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure.