Inverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential

Document Type : Research Articles


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


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