On a nonlocal non-linear inverse scattering problem

TL;DR

This paper investigates the inverse scattering problem for a nonlinear fractional Helmholtz equation in three dimensions, aiming to recover a potential from scattering data, contributing to the mathematical understanding of nonlinear inverse problems.

Contribution

It introduces a novel analysis of the inverse scattering problem for a nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions.

Findings

Established conditions for potential recovery from scattering amplitude.

Extended inverse scattering theory to nonlinear fractional PDEs.

Provided mathematical framework for future numerical methods.

Abstract

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.