Inverse scattering problem for the fifth-order Schr${\rm\bf\ddot{o}}$dinger operator on the whole axis

Abstract

A method of solution for the inverse scattering problem for the linear fifth order Schr${\rm\ddot{o}}$dinger operator is found. Two closed systems of linear singular integral equations are obtained. From solutions to these equations, potential on the left and right half-axes is restored unambiguously.