Modified Homotopic approach for diffractive production

TL;DR

This paper reviews the application of the homotopy method to solve a simplified non-linear evolution equation in diffractive production during deep inelastic scattering, showing small non-linear corrections.

Contribution

It introduces a modified homotopic approach that incorporates non-linear corrections into the linear evolution equation and provides an analytical solution.

Findings

Non-linear corrections are small and manageable.

Analytical solutions are obtained for the simplified evolution equation.

The method facilitates understanding of diffractive production dynamics.

Abstract

We review the recent developments of 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.