Inverse scattering for the fractional Schr\"{o}dinger equation
Analysis of PDEs
2025-09-17 v1
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 (,)-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.
Keywords
Cite
@article{arxiv.2509.12685,
title = {Inverse scattering for the fractional Schr\"{o}dinger equation},
author = {Saumyajit Das and Tuhin Ghosh and Shiqi Ma},
journal= {arXiv preprint arXiv:2509.12685},
year = {2025}
}
Comments
19 pages