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Trudy Mat. Inst. Steklova, 2005, Volume 251, Pages 10–53 (Mi tm44)  

This article is cited in 2 scientific papers (total in 2 papers)

Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential

M. Boitia, F. Pempinellia, A. K. Pogrebkovb, B. Prinari

a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We derive and describe in detail the extension of the inverse scattering transform method to the case of linear spectral problems with potentials that do not decay in some space directions. Our presentation is based on the extended resolvent approach. As a basic example, we consider the nonstationary Schrödinger equation with a potential that is a perturbation of a generic one-dimensional potential by means of a decaying function of two variables. We give the corresponding modifications of the Jost solutions and the spectral data and derive their properties and characterization equations.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 251, 6–48

Bibliographic databases:
UDC: 530.1
Received in January 2005

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential”, Nonlinear dynamics, Collected papers, Trudy Mat. Inst. Steklova, 251, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 10–53; Proc. Steklov Inst. Math., 251 (2005), 6–48

Citation in format AMSBIB
\Bibitem{BoiPemPog05}
\by M.~Boiti, F.~Pempinelli, A.~K.~Pogrebkov, B.~Prinari
\paper Spectral Theory of the Nonstationary Schr\"odinger Equation with a~Bidimensionally Perturbed One-Dimensional Potential
\inbook Nonlinear dynamics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 251
\pages 10--53
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm44}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2234376}
\zmath{https://zbmath.org/?q=an:1123.35051}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 251
\pages 6--48


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    This publication is cited in the following articles:
    1. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential”, Theoret. and Math. Phys., 144:2 (2005), 1100–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Boiti M., Pempinelli F., Pogrebkov A.K., “Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed $N$-soliton potential”, J. Math. Phys., 47:12 (2006), 123510, 43 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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