INVERSE SCATTERING PROBLEM FOR THE ·IMPULSIVE SCHRÖDINGER EQUATION WITH A POLYNOMIAL SPECTRAL DEPENDENCE IN THE POTENTIAL

Document Type: Research articles

Authors

Department of Mathematics, Faculty of Sciences, Cumhuriyet University, 58140, Sivas, Turkey

Abstract

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructing of the potential functions of the equation in that case when there is no a discrete spectrum

Keywords