PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, vol.49, no.2, pp.268-274, 2023 (ESCI)
The perturbed Airy equation -y ''- xy + q(x)y = lambda y on the half-axis 0 <= x < +infinity with the y '(0) = hy(0) boundary condition is considered. By means of transformation operators the direct and inverse scattering problems are studied. We obtain the main integral equation of the inverse problem. An effective algorithm for reconstruction of perturbed potential is indicated.