Constructive solution to inverse scattering problem for differential systems with a singularity (Q6115274)

The system of equations \[ y' = (\rho B+ x^{-1}A + q(x))y \] with \(B\) being an \(n\times n\) diagonal matrix, \(A\) being an \(n\times n\) matrix, \(q\) being the potential, and \(\rho\) the spectral parameter is considered. This system is close to the scalar differential equation of \(n\)-th order with coefficients diverging for \(x=0\). The inverse problem for the above system is investigated. The author obtains the reconstruction formula for finding the potential from the scattering data.