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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 93, Number 2, Pages 181–210 (Mi tmf1522)  
This article is cited in 23 scientific papers (total in 23 papers)

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and KPI equation

M. Boitia, F. Pempinellia, A. K. Pogrebkovb, M. K. Polivanov

a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (2331 kB) Citations (23)
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Abstract: The resolvent operator of the Linear Problem is determined as full Green function continued in the complex domain in two variables. An analog of the known Hilbert Identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the Nonstationary Schrödinger Equation as an example we show that all types of solutions of the Linear Problem as well as Spectral Data known in the literature are given as specific values of this unique function — resolvent. New form of Inverse Problem is formulated.
Received: 28.09.1992
English version:
Theoretical and Mathematical Physics, 1992, Volume 93, Issue 2, Pages 1200–1224
DOI: https://doi.org/10.1007/BF01083519
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. K. Polivanov, “Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and KPI equation”, TMF, 93:2 (1992), 181–210; Theoret. and Math. Phys., 93:2 (1992), 1200–1224
Citation in format AMSBIB
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\by M.~Boiti, F.~Pempinelli, A.~K.~Pogrebkov, M.~K.~Polivanov
\paper Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schr\"odinger problem and KPI equation
\jour TMF
\yr 1992
\vol 93
\issue 2
\pages 181--210
\mathnet{http://mi.mathnet.ru/tmf1522}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1233541}
\zmath{https://zbmath.org/?q=an:0806.35131}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 93
\issue 2
\pages 1200--1224
\crossref{https://doi.org/10.1007/BF01083519}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992LJ23200001}
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  • https://www.mathnet.ru/eng/tmf1522
  • https://www.mathnet.ru/eng/tmf/v93/i2/p181
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:468
    Full-text PDF :150
    References:69
    First page:3
     
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