Article

Inverse problem of scattering theory for a class one-dimensional Schrödinger equation

Published in: Quaestiones Mathematicae
Volume 42 , issue 7 , 2019 , pages: 841–856

DOI: 10.2989/16073606.2018.1498814

Author(s): Kh.R. Mamedov Mathematics Department, Science and Letters Faculty, Turkey , A.A. Nabiev Computer Engineering Department, Engineering Faculty, Turkey

Keywords: 34A55 , 34L25 , 34L40 , 34A55 , 34L25 , 34L40

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Abstract

In this work, direct and inverse scattering problem on the real axis for the Schrödinger equation with piecewise-constant coefficient are studied. Using the new integral representations for solutions, the scattering data is defined, the main integral equations of the inverse scattering problem are obtained, the spectral characteristics of the scattering data are investigated and uniqueness theorem for the solution of inverse problem is proved.

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