Aktosun, Tuncay Scattering and inverse scattering for a second-order differential equation. (English) Zbl 0773.34011 J. Math. Phys. 34, No. 5, 1619-1634 (1993). Summary: The scattering and three inverse scattering problems for \((d/dx)[a(x)(d\psi/dx)]+k^ 2h(x)\psi=Q(x)\psi\) on the real axis are considered herein. In the first inverse scattering problem, \(Q(x)\) is recovered when \(a(x)\), \(h(x)\), and the scattering data are given. In the second inverse problem \(h(x)\) is recovered when \(a(x)\), \(Q(x)\), and the scattering data are known. In the third inverse problem, in case \(Q(x)=0\), \(a(x)\) is recovered when \(h(x)\) and the scattering data are known. The inversion is illustrated with examples. Cited in 3 Documents MSC: 34A55 Inverse problems involving ordinary differential equations 34L25 Scattering theory, inverse scattering involving ordinary differential operators Keywords:second-order differential equation; inverse scattering problems; inverse problem PDF BibTeX XML Cite \textit{T. Aktosun}, J. Math. Phys. 34, No. 5, 1619--1634 (1993; Zbl 0773.34011) Full Text: DOI OpenURL References: [1] Faddeev L. D., Am. Math. Soc. Transl. 2 pp 139– (1964) [2] Faddeev L. D., Tr. Mat. Inst. Stekl. 73 pp 314– (1964) [3] DOI: 10.1063/1.524447 · Zbl 0446.34029 [4] DOI: 10.1063/1.529650 · Zbl 0760.35032 [5] DOI: 10.1063/1.529714 · Zbl 0756.34083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.