Inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential

Abstract

In the present paper the inverse scattering problem for the Schrodinger-type equation with a polynomial energy-dependent potential is investigated on the entire real line (−∞; + ∞). The scattering data of the scattering problem are defined and the properties of the data are studied. The system of the main integral equations of the scattering problem is derived and the potential functions are recovered.