Mathematical Sciences: Multidimensional Inverse Scattering Problems

数学科学：多维逆散射问题

• 批准号: 9217627
• 负责人: Tuncay Aktosun
• 金额: $ 6.14万
• 依托单位: North Dakota State University Fargo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9217627&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multidimensional; Inverse; Scattering

This project consists of an investigation of the inverse scattering problems for the multidimensional Schrodinger equations when the potential is independent of energy and when the potential is proportional to energy. In the former case, the Wiener-Hopf factorization and the generalized Muskhelishvili- Vekua technique will be used to investigate the characterization of the scattering data, the relationship between bound states and partial indices, the inversion from partial data, and the stability of the inversion. In the latter case, the inverse scattering problem will be formulated as a Riemann-Hilbert problem with a discontinuity of almost periodic type and its solution will be obtained through a generalized Wiener-Hopf factorization technique. The solution of the inverse scattering problem with energy- independent potentials is equivalent to determining molecular, atomic, and nuclear forces in terms of the scattering data obtained in collision experiments, and the determination of these forces is one of the fundamental problems in physics. The inverse scattering problem with energy-dependent potentials is equivalent to the determination of the properties of a medium using only the measurements made on the boundary; such a problem has many important applications in wave propagation, seismology, nondestructive testing, oil exploration, atmospheric profile inversion, and other areas.

这个项目包括一个调查的逆 多维薛定谔散射问题 当势与能量无关且当 势能与能量成正比。 在前一种情况下， Wiener-Hopf分解和广义Muskhelishvili- Vekua技术将用于研究表征 的散射数据，束缚态之间的关系， 部分索引，部分数据的反演，以及 反演的稳定性。 在后一种情况下， 散射问题将被公式化为黎曼-希尔伯特 一个概周期型间断问题及其 解将通过广义Wiener-Hopf 因式分解技术 具有能量的逆散射问题的解- 独立势等效于确定分子， 根据散射数据计算原子力和核力 在碰撞实验中获得，并确定这些 力是物理学的基本问题之一。 的 具有能量依赖势的逆散射问题， 相当于确定介质的性质 仅使用边界上的测量;这样的问题 在波传播，地震学， 无损检测，石油勘探，大气剖面 反转和其他领域。