Iterative methods for solving the inverse problem in potential scattering theory

An analytic investigation is made of the solution of the inverse scattering problem for the radial Schroedinger equation on the basis of the equation for the continuous analog of Newton's method. It is shown that some of the equations obtained here admit first integrals analogous to those known for the Korteweg-de Vries equation. A stable iterative algorithm is proposed for finding the potential from the scattering data.