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arXiv · 2610.14978

Uniqueness and stability for inverse potential scattering with multiple wavenumbers

Dong Qiu·Xiang Xu·Yue Zhao
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Abstract

This paper is concerned with the inverse scattering problem of determining a real-valued potential for the three-dimensional Schrödinger equation from multi-wavenumber data. Under suitable a priori bounds, we establish local increasing stability from near-field Dirichlet data on a fixed sphere for polynomially decaying potentials, and global increasing stability from full far-field amplitudes for exponentially decaying potentials. The stability estimates consist of a noise term and a remainder term, with the latter decreasing as the upper measured wavenumber increases. We also obtain global uniqueness from exact near-field data under weaker regularity assumptions. The analysis combines analytic continuation, weighted resolvent estimates, and half-ray identities whose differences at chord endpoints cancel the unknown exterior contribution.

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Dong Qiu, Xiang Xu, Yue Zhao. 2026-10-10. Uniqueness and stability for inverse potential scattering with multiple wavenumbers. https://arxiv.org/abs/2610.14978

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