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Mathematics of the USSR-Izvestiya, 1986, Volume 26, Issue 3, Pages 479–496
DOI: https://doi.org/10.1070/IM1986v026n03ABEH001156 (Mi im1364) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves

M. V. Babich, A. I. Bobenko, V. B. Matveev
English version PDF (922 kB) Citations (18)
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DOI: https://doi.org/10.1070/IM1986v026n03ABEH001156
Abstract: A new approach is given for extracting from general formulas of finite-zone integration solutions of genus $g\geqslant2$ expressible in terms of one-dimensional theta functions. As an application general formulas fo the type of the Lamb Ansatz for genus $g=3$ are found for the sine-Gordon, nonlinear Schrödinger and Koretweg–de Vries equations, and the period matrices of some hyperelliptic curves are computed explicitly.
Bibliography: 35 titles.
Received: 29.06.1983
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1985, Volume 49, Issue 3, Pages 511–529
Bibliographic databases:
UDC: 517.43+519.46
MSC: Primary 35Q20; Secondary 35J10, 35R30, 14K25
Language: English
Original paper language: Russian
Citation: M. V. Babich, A. I. Bobenko, V. B. Matveev, “Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves”, Izv. Akad. Nauk SSSR Ser. Mat., 49:3 (1985), 511–529; Math. USSR-Izv., 26:3 (1986), 479–496
Citation in format AMSBIB
\Bibitem{BabBobMat85}
\by M.~V.~Babich, A.~I.~Bobenko, V.~B.~Matveev
\paper Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 3
\pages 511--529
\mathnet{http://mi.mathnet.ru/im1364}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=794954}
\zmath{https://zbmath.org/?q=an:0657.35021|0583.35012}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 3
\pages 479--496
\crossref{https://doi.org/10.1070/IM1986v026n03ABEH001156}
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  • https://doi.org/10.1070/IM1986v026n03ABEH001156
  • https://www.mathnet.ru/eng/im/v49/i3/p511
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:817
    Russian version PDF:238
    English version PDF:20
    References:65
    First page:2
     
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