This article is cited in 3 papers

Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential

M. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov^b, B. Prinari<sup>a

a</sup> Lecce University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the nonstationary Schrodinger equation with the potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function in the framework of the extended resolvent approach. We give the corresponding modification of the Jost and advanced/retarded solutions and spectral data and present relations between them.

Keywords: inverse scattering transform, resolvent approach, Kadomtsev–Petviashvili equation.

DOI: 10.4213/tmf1851

 English version: Theoretical and Mathematical Physics, 2005, 144:2, 1100–1116

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