Inverse scattering problem for a family of phase-equivalent nonlocal potentials

General statement of the inverse scattering problem as applied to the Schrodinger equation with nonlocal potentials is proposed for a family of phase-equivalent nonlocal potentials. The main result is that the problem of reconstructing both the family of phase-equivalent wavefunctions and the corresponding family of phase-equivalent potentials is reduced to solving some regular (quadratically nonlinear) integral equation. It is shown that if the S-matrix S l (k) is rational in k, then for a dense set of nonlocal potentials the main equation turns into a system of second-order algebraic equations, and the corresponding potentials become separable. To illustrate this approach in more detail the author gives an exhaustive description of the family of transparent potentials.