N-fold scattering series for Kolmogorov equation

TL;DR

This paper develops a series solution for the Kolmogorov equation modeling particle scattering, proves its convergence, and applies it to light scattering and LIDAR problems.

Contribution

It introduces a multiple scattering series expansion for the Kolmogorov equation and provides convergence proofs, with applications to optical scattering problems.

Findings

Series solution converges for the Kolmogorov equation.

Integral representation facilitates estimations.

Application demonstrated in light scattering and LIDAR contexts.

Abstract

We consider a formulation of initial problem for Kolmogorov equation that corresponds a localized source of particles to be scattered by medium with given scattering amplitude density (scattering indicatrix). The multiple scattering expansion and amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the multiple integral representation for the series terms, transform it into a form, convenient for estimations and prove convergence of the series. An application to light beam scattering and LIDAR problem solution is outlined.