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

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

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
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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
2. Peter D. Lax, “Mathematics and its applications”, Math Intelligencer, 8:4 (1986), 14
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
4. Y. Kitazawa, “Explicit parametrizations of degenerate surfaces from the KP equation and closed bosonic string amplitudes”, Nuclear Physics B, 297:2 (1988), 338
5. Peter D. Lax, “The Flowering of Applied Mathematics in America”, SIAM Rev, 31:4 (1989), 533
6. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225
7. I. A. Taimanov, “Prym varieties of branched coverings and nonlinear equations”, Math. USSR-Sb., 70:2 (1991), 367–384
8. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218
9. Robert Carroll, Jen Hsu Chang, “The whitham equations revisited”, Applicable Analysis, 64:3-4 (1997), 343
10. A S Fokas, “Lax pairs: a novel type of separability”, Inverse Probl, 25:12 (2009), 123007
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