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

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:

One dimensional Schrödinger equation , scattering data , Jost solution , direct problem , inverse scattering problem