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Mat. Sb. (N.S.), 1987, Volume 133(175), Number 3(7), Pages 382–391 (Mi msb2574)  

This article is cited in 26 scientific papers (total in 26 papers)

A matrix analogue of Appell's theorem and reductions of multidimensional Riemann theta-functions

A. O. Smirnov


Abstract: The purpose of this paper is to determine a simple and efficient method of reduction of Riemann theta-functions of large genus to Riemann theta-functions of smaller genus.
Figures: 1.
Bibliography: 15 titles.

Full text: PDF file (491 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1988, 61:2, 379–388

Bibliographic databases:

UDC: 517.43+517.98
MSC: Primary 14K25, 30F99; Secondary 35Q20
Received: 11.02.1985 and 01.12.1986

Citation: A. O. Smirnov, “A matrix analogue of Appell's theorem and reductions of multidimensional Riemann theta-functions”, Mat. Sb. (N.S.), 133(175):3(7) (1987), 382–391; Math. USSR-Sb., 61:2 (1988), 379–388

Citation in format AMSBIB
\Bibitem{Smi87}
\by A.~O.~Smirnov
\paper A~matrix analogue of Appell's theorem and reductions of multidimensional Riemann theta-functions
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 3(7)
\pages 382--391
\mathnet{http://mi.mathnet.ru/msb2574}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=909858}
\zmath{https://zbmath.org/?q=an:0677.33002|0626.33002}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 2
\pages 379--388
\crossref{https://doi.org/10.1070/SM1988v061n02ABEH003213}


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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, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, Theoret. and Math. Phys., 78:1 (1989), 6–13  mathnet  crossref  mathscinet  isi
    2. A. O. Smirnov, “Real elliptic solutions of the “sine-Gordon” equation”, Math. USSR-Sb., 70:1 (1991), 231–240  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Matveev V., Smirnov A., “Some Comments on the Solvable Chiral Potts-Model”, Lett. Math. Phys., 19:3 (1990), 179–185  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. Smirnov A., “Finite-Gap Elliptic Solutions of the KdV Equation”, Acta Appl. Math., 36:1-2 (1994), 125–166  crossref  mathscinet  zmath  isi
    6. A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743  mathnet  crossref  mathscinet  zmath  isi
    7. Fritz Gesztesy, Rudi Weikard, “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”, Acta Math, 181:1 (1998), 63  crossref  mathscinet  zmath  isi
    8. Ronnie Dickson, Fritz Gesztesy, Karl Unterkofler, “A New Approach to the Boussinesq Hierarchy”, Math Nachr, 198:1 (1999), 51  crossref
    9. R. DICKSON, F. GESZTESY, K. UNTERKOFLER, “ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY”, Rev. Math. Phys, 11:07 (1999), 823  crossref
    10. Xianguo Geng, Lihua Wu, Guoliang He, “Quasi-Periodic Solutions of Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem”, Studies in Applied Mathematics, 2011, no  crossref
    11. Xianguo Geng, Lihua Wu, Guoliang He, “Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions”, Physica D: Nonlinear Phenomena, 2011  crossref
    12. A. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, Theoret. and Math. Phys., 173:1 (2012), 1403–1416  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    13. Lihua Wu, Guoliang He, Xianguo Geng, “Algebro-geometric solutions to the modified Sawada-Kotera hierarchy”, J. Math. Phys, 53:12 (2012), 123513  crossref
    14. Lihua Wu, Guoliang He, Xianguo Geng, “Quasi-periodic solutions to the two-component nonlinear Klein–Gordon equation”, Journal of Geometry and Physics, 2012  crossref
    15. Xianguo Geng, Lihua Wu, Guoliang He, “Quasi-periodic Solutions of the Kaup–Kupershmidt Hierarchy”, J Nonlinear Sci, 2013  crossref
    16. A. Cabada, A. Yakhshimuratov, “The System of Kaup Equations with a Self-Consistent Source in the Class of Periodic Functions”, Zhurn. matem. fiz., anal., geom., 9:3 (2013), 287–303  mathnet  mathscinet
    17. A. O. Smirnov, “Periodic Two-Phase “Rogue Waves””, Math. Notes, 94:6 (2013), 897–907  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407  mathnet
    19. Xianguo Geng, Yunyun Zhai, H.H. Dai, “Algebro-geometric solutions of the coupled modified Korteweg–de Vries hierarchy”, Advances in Mathematics, 263 (2014), 123  crossref
    20. Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova, “Three-Phase Freak Waves”, SIGMA, 11 (2015), 032, 14 pp.  mathnet  crossref  mathscinet
    21. Lihua Wu, Guoliang He, Xianguo Geng, “A note on the quasi-periodic solutions of the modified Boussinesq hierarchy”, Journal of Geometry and Physics, 2015  crossref
    22. Hui Wang, Xianguo Geng, “Algebro-geometric solutions to a new hierarchy of soliton equations”, Zhurn. matem. fiz., anal., geom., 11:4 (2015), 359–398  mathnet  crossref  mathscinet
    23. Xianguo Geng, Xin Zeng, “Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy”, Theoret. and Math. Phys., 190:1 (2017), 18–42  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    24. Geng X., Wang H., “Algebro-geometric constructions of quasi-periodic flows of the Newell hierarchy and applications”, IMA J. Appl. Math., 82:1 (2017), 97–130  crossref  mathscinet  isi  scopus
    25. V. B. Matveev, A. O. Smirnov, “Dvukhfaznye periodicheskie resheniya uravnenii iz AKNS ierarkhii”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 205–227  mathnet
    26. X. Geng, J. Wei, X. Zeng, “Algebro-geometric integration of the modified Belov–Chaltikian lattice hierarchy”, Theoret. and Math. Phys., 199:2 (2019), 675–694  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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