This article is cited in 6 papers

On the Jost solutions for a class of Schrödinger equations with piecewise constant coefficients

A. A. Nabiev^a, Kh. R. Mamedov<sup>b

a</sup> Department of Mathematics, Faculty of Science, Cumhuriyet University, Sivas, 58140 Turkey
^b Department of Mathematics, Faculty of Science and Letters, Mersin University, Mersin, 33343 Turkey

Abstract: In this paper, the new integral representations for the Jost solutions of the one-dimensional Schrödinger equation with the piecewise-constant leading coefficient are obtained. The connections, obtained between the kernel functions of the integral representations and the potential function of the Schrödinger equation, enable to solve the inverse scattering problem on the entire real line.

Key words and phrases: Schrödinger equation, Jost solution, integral representation.

MSC: 34L40

Received: 23.10.2013
Revised: 03.08.2014

Language: English

DOI: 10.15407/mag11.03.279

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