固定角度散射振幅下的高阶薛定谔算子反向散射问题

IF 1.4 4区物理与天体物理 Q2 MATHEMATICS, APPLIED

Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-05 DOI:10.1007/s44198-023-00158-w

Hua Huang, Huizhen Li, Zhigang Zhou

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引用次数: 0

摘要

我们考虑了高阶薛定谔算子\(H=(-\Delta )^m+q(x)\)的反散射问题，\(m=1,2,3,\ldots\)。我们证明了在某些假设条件下，H 在固定角度的散射振幅可以唯一地决定势q(x)，这扩展了关于这个问题的早期结果。q(x)的唯一性主要取决于Born近似序列的构造及其估计。

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Inverse Scattering Problem for the High Order Schrödinger Operator at Fixed Angles Scattering Amplitude

We consider the inverse scattering problem for the higher order Schrödinger operator \(H=(-\Delta )^m+q(x)\), \(m=1,2, 3,\ldots\). We show that the scattering amplitude of H at fixed angles can uniquely determines the potential q(x) under certain assumptions, which extends the early results on this problem. The uniqueness of q(x) mainly depends on the construction of the Born approximation sequence and its estimation.

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来源期刊

Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics