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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 1015–1028 (Mi izv1596)  

This article is cited in 10 scientific papers (total in 10 papers)

The Kadomtsev–Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces

B. A. Dubrovin


Abstract: S. P. Novikov's conjecture that the relations between theta functions that follow from the nonlinear Kadomtsev–Petviashvili equation, well known in mathematical physics, characterize the Jacobian varieties of Riemann surfaces among all Abelian varieties is proved in this paper, except for the possibility of superfluous components.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 285–296

Bibliographic databases:

UDC: 513.835
MSC: Primary 14K20, 14K25, 14K30; Secondary 32G20
Received: 13.04.1981

Citation: B. A. Dubrovin, “The Kadomtsev–Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 1015–1028; Math. USSR-Izv., 19:2 (1982), 285–296

Citation in format AMSBIB
\Bibitem{Dub81}
\by B.~A.~Dubrovin
\paper The Kadomtsev--Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 1015--1028
\mathnet{http://mi.mathnet.ru/izv1596}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637614}
\zmath{https://zbmath.org/?q=an:0501.14016|0477.14018}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 285--296
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001418}


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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. Takahiro Shiota, “Characterization of Jacobian varieties in terms of soliton equations”, Invent math, 83:2 (1986), 333  crossref  mathscinet  isi
    2. Peter D. Lax, “Mathematics and its applications”, Math Intelligencer, 8:4 (1986), 14  crossref  mathscinet
    3. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Russian Math. Surveys, 41:2 (1986), 1–49  mathnet  crossref  mathscinet  zmath  isi
    4. Y. Kitazawa, “Explicit parametrizations of degenerate surfaces from the KP equation and closed bosonic string amplitudes”, Nuclear Physics B, 297:2 (1988), 338  crossref
    5. Peter D. Lax, “The Flowering of Applied Mathematics in America”, SIAM Rev, 31:4 (1989), 533  crossref  mathscinet  zmath  isi
    6. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. I. A. Taimanov, “Prym varieties of branched coverings and nonlinear equations”, Math. USSR-Sb., 70:2 (1991), 367–384  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Robert Carroll, Jen Hsu Chang, “The whitham equations revisited”, Applicable Analysis, 64:3-4 (1997), 343  crossref
    10. A S Fokas, “Lax pairs: a novel type of separability”, Inverse Probl, 25:12 (2009), 123007  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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