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arXiv · 2509.12685

Inverse scattering for the fractional Schr\"{o}dinger equation

Saumyajit Das·Tuhin Ghosh·Shiqi Ma
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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.

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Saumyajit Das, Tuhin Ghosh, Shiqi Ma. 2025-09-16. Inverse scattering for the fractional Schr\"{o}dinger equation. https://arxiv.org/abs/2509.12685

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