Towards spectral theory of the Nonstationary Schr\"{o}dinger equation   with a two-dimensionally perturbed one-dimensional potential
  The Nonstationary Schr\"{o}dinger equation with potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function is considered here in the framework of the extended resolvent approach. The properties of the Jost solutions and spectral data are investigated. 
M.Boiti, F.Pempinelli, A.K.Pogrebkov, B.Prinari