Stability of direct and inverse scattering problems for the self-adjoint Schrödinger operators on the half-line (Q2033240)

The author of this article considers the Schrödinger equation \(-y''(x)+q(x)y(x)=k^2y(x)\) on the half-line (\(y>0\)) with the self-adjoint boundary condition \(y'(0)\sin \theta+y(0)\cos\theta=0\), where \(\theta \in (0,\pi]\), the parameter \(k^2\) is the spectral parameter, and \(q(x)\) is real-valued function satisfying \(\int_0^\infty (1+x)^j|q(x)|\,\mathrm{d}x<\infty\). On the one hand, an estimate for the difference of the reflection coefficients is provided as the difference of the corresponding potentials and the parameters in the coundary conditions. On the other hand, an estimate is given for the difference of the potentials as the difference of the corresponding scattering data.