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Sibirsk. Mat. Zh., 2003, Volume 44, Number 4, Pages 870–882 (Mi smj1220)  

This article is cited in 5 scientific papers (total in 5 papers)

On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves

I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We describe a wide class of two-dimensional potential Schrödinger and Dirac operators which are finite-gap at the zero energy level and whose spectral curves at this level are singular, in particular may have $n$-multiple points with $n\geqslant3$.

Keywords: Schrödinger operator, Dirac operator, spectral curve, finite-gap integration

Full text: PDF file (242 kB)
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English version:
Siberian Mathematical Journal, 2003, 44:4, 686–694

Bibliographic databases:

UDC: 517.95
Received: 29.10.2002

Citation: I. A. Taimanov, “On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves”, Sibirsk. Mat. Zh., 44:4 (2003), 870–882; Siberian Math. J., 44:4 (2003), 686–694

Citation in format AMSBIB
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\by I.~A.~Taimanov
\paper On two-dimensional finite-gap potential Schr\"odinger and Dirac operators with singular spectral curves
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 4
\pages 870--882
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2010133}
\zmath{https://zbmath.org/?q=an:1091.34557}
\elib{http://elibrary.ru/item.asp?id=14006795}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 4
\pages 686--694
\crossref{https://doi.org/10.1023/A:1024792708878}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184886500014}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Taimanov IA, “Finite-gap theory of the Clifford torus”, International Mathematics Research Notices, 2005, no. 2, 103–120  crossref  mathscinet  zmath  isi  elib
    2. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. E. Mironov, I. A. Taimanov, “Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves”, Proc. Steklov Inst. Math., 255 (2006), 169–184  mathnet  crossref  mathscinet
    4. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. McIntosh I., “The Quaternionic KP Hierarchy and Conformally Immersed 2-Tori in the 4-Sphere”, Tohoku Math J (2), 63:2 (2011), 183–215  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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