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TMF, 1990, Volume 84, Number 1, Pages 38–45 (Mi tmf5859)  

This article is cited in 6 scientific papers (total in 6 papers)

Elliptic solutions of nonlinear equations

I. A. Taimanov


Abstract: A method is described for constructing algebraic curves whose theta functions reduce to one-dimensional functions. This makes it possible to construct finite-gap solutions of nonlinear equations expressed in terms of the elliptic functions. Elliptic two-gap potentials of the Schrödinger operator different from the Lamé and Verdier potentials are constructed.

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English version:
Theoretical and Mathematical Physics, 1990, 84:1, 700–706

Bibliographic databases:

Received: 18.07.1989

Citation: I. A. Taimanov, “Elliptic solutions of nonlinear equations”, TMF, 84:1 (1990), 38–45; Theoret. and Math. Phys., 84:1 (1990), 700–706

Citation in format AMSBIB
\Bibitem{Tai90}
\by I.~A.~Taimanov
\paper Elliptic solutions of~nonlinear equations
\jour TMF
\yr 1990
\vol 84
\issue 1
\pages 38--45
\mathnet{http://mi.mathnet.ru/tmf5859}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1070345}
\zmath{https://zbmath.org/?q=an:0760.35021}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 84
\issue 1
\pages 700--706
\crossref{https://doi.org/10.1007/BF01017194}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990FA15100004}


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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. A. O. Smirnov, “Elliptic solutions of the nonlinear Schrödinger equation and the modified Korteweg–de Vries equation”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 461–470  mathnet  crossref  mathscinet  zmath  isi
    2. A. O. Smirnov, “Solutions of the KdV equation elliptic in $t$”, Theoret. and Math. Phys., 100:2 (1994), 937–947  mathnet  crossref  mathscinet  zmath  isi
    3. A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743  mathnet  crossref  mathscinet  zmath  isi
    4. A. O. Smirnov, “Elliptic in $t$ solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 107:2 (1996), 568–578  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271  crossref  mathscinet  zmath  isi
    6. B. T. Saparbaeva, “Two-Dimensional Finite-Gap Schrödinger Operators with Elliptic Coefficients”, Math. Notes, 747–749  mathnet  crossref  crossref  mathscinet  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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