We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to given scattering amplitude in the class of separable potentials.
Uniqueness of the solution to inverse scattering problem with backscattering data
Uniqueness theorem for inverse scattering problem with non-overdetermined data
Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave
