Inverse scattering for the fractional Schrödinger equation

2025/09/16 by Saumyajit Das, Das, Saumyajit, Tuhin Ghosh +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2509.12685

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

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.

Citations

• Recovering asymptotics of potentials from the scattering of relativistic Schrödinger operators
• Fractional Borg-Levinson Problem with small non-negative potential of small growth
• The Calderón problem for nonlocal operators
• Fixed angle inverse scattering for almost symmetric or controlled perturbations
• Uniqueness for the inverse fixed angle scattering problem
• Green's formula and a Dirichlet-to-Neumann operator for fractional-order\n pseudodifferential operators
• Remarks on L^p-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems
• Recent progress of inverse scattering theory on non-compact manifolds

Cited by

• The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness

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