Scattering and inverse scattering for a second-order differential equation. (English) Zbl 0773.34011

Aktosun, Tuncay

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.

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

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