Inverse scattering problem on the semi-axis for a system of six ordinary differential equations

In this article, the inverse scattering problem of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. For an ordinary system of six equations on a semi-axis, under joint consideration of four problems the inverse scattering problem on a first approximation was solved. The coefficients of the considered system are uniquely determined by the scattering matrix on a semi-axis.