Inverse scattering for the fractional Schr\"odinger equation
Abstract
This article is devoted to studying the inverse scattering for the fractional Schr\"odinger 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 Schr\"odinger equation. We prove the uniqueness of the potential using the scattering amplitude data.
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