Inverse scattering for the fractional Schrödinger equation

Abstract

This article is devoted to studying the inverse scattering for the fractional Schrödinger equation, and in particular we solve the Born approximation problem. Based on the ($p$,$q$)-type resolvent estimate for the fractional Laplacian, we derive an expression for the scattering amplitude of the scattered solution of the fractional Schrödinger equation. We prove the uniqueness of the potential using the scattering amplitude data.

23 pages