Born and Inverse Born Series for a Special Case of the Second Harmonic Generation Problem

TL;DR

This paper analyzes the Born and inverse Born series for a specific second harmonic generation PDE system, providing recursive formulas, convergence conditions, and fixed point analysis to improve understanding of their applicability.

Contribution

It introduces explicit recursive formulas and convergence criteria for the Born and inverse Born series in a special second harmonic generation problem.

Findings

Derived recursive formulas for forward operators

Established boundedness and convergence conditions

Applied fixed point theory for convergence analysis

Abstract

We study the Born and Inverse Born series for a special case of the second harmonic generation system of PDEs. We give a recursive formula for the forward operators and prove boundedness conditions that guarantee the convergence of the Born and inverse Born series. We also use fixed point theory to give explicit conditions for convergence of the Born series.