On the scattering inverse problem for the differential operators of high order on the semi-axis

On semi-axis $(0, \infty)$ the self-adjoint differential operator of even order $2n>2$ is considered with the coefficients, convergent to the finite limit at the infinity. In conditions, providing the existence of the transform operator, the scattering data of $L$ operator are introduced, which are some of its spectral characteristics. Scattering inverse problem is raised, requiring the restoration of $L$ according to its scattering data. Solving the linear integral equation on the kernel of the transform operator an effective method for restoration of $L$ by the scattering data is developed. The uniqueness of such restoration is proved.