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TMF, 2005, Volume 144, Number 2, Pages 257–276 (Mi tmf1851)  

This article is cited in 3 scientific papers (total in 3 papers)

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

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

a 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: https://doi.org/10.4213/tmf1851

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

Bibliographic databases:


Citation: 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”, TMF, 144:2 (2005), 257–276; Theoret. and Math. Phys., 144:2 (2005), 1100–1116

Citation in format AMSBIB
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\paper Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential
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\jour Theoret. and Math. Phys.
\yr 2005
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\pages 1100--1116
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  • http://mi.mathnet.ru/eng/tmf1851
  • https://doi.org/10.4213/tmf1851
  • http://mi.mathnet.ru/eng/tmf/v144/i2/p257

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Boiti M, Pempinelli F, Pogrebkov AK, “On the extended resolvent of the nonstationary Schrodinger operator for a Darboux transformed potential”, Journal of Physics A-Mathematical and General, 39:8 (2006), 1877–1898  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Boiti M, Pempinelli F, Pogrebkov AK, “Scattering transform for nonstationary Schrodinger equation with bidimensionally perturbed N-soliton potential”, Journal of Mathematical Physics, 47:12 (2006), 123510  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Building an extended resolvent of the heat operator via twisting transformations”, Theoret. and Math. Phys., 159:3 (2009), 721–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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