Inverse scattering for the fractional Schrödinger equation
Saumyajit Das, Tuhin Ghosh, Shiqi Ma
公開日: 2025/9/16
Abstract
This article is devoted to studying the inverse scattering for the fractional Schr\"{o}dinger 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\"{o}dinger equation. We prove the uniqueness of the potential using the scattering amplitude data.