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Russian Mathematical Surveys, 2021, Volume 76, Issue 4, Pages 587–652
DOI: https://doi.org/10.1070/RM10007 (Mi rm10007) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Surveys

Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves

V. M. Buchstabera, A. V. Mikhailovbc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b University of Leeds, Leeds, UK
c Centre of Integrable Systems, P.G. Demidov Yaroslavl State University
English version PDF (870 kB) Citations (7) Russian version article
References:
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DOI: https://doi.org/10.1070/RM10007
Abstract: This survey is devoted to integrable polynomial Hamiltonian systems associated with symmetric powers of plane algebraic curves. We focus our attention on the relations (discovered by the authors) between the Stäckel systems, Novikov's equations for the $g$th stationary Korteweg–de Vries hierarchy, the Dubrovin–Novikov coordinates on the universal bundle of Jacobians of hyperelliptic curves, and new systems obtained by considering the symmetric powers of curves when the power is not equal to the genus of the curve.
Bibliography: 52 titles.
Keywords: polynomial Hamiltonian systems, Stäckel systems, Korteweg–de Vries hierarchy, symmetric powers of curves, Abelian functions, systems of hydrodynamical type.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1397
EPSRC EP/V050451/1
The research of the second author was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation (contract no. 075-02-2021-1397) and the Engineering and Physical Sciences Research Council (grant no. EP/V050451/1).
Received: 10.05.2021
Bibliographic databases:
Document Type: Article
UDC: 517.938+512.77
MSC: 14H70, 14K25, 37J35
Language: English
Original paper language: Russian
Citation: V. M. Buchstaber, A. V. Mikhailov, “Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves”, Russian Math. Surveys, 76:4 (2021), 587–652
Citation in format AMSBIB
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\paper Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves
\jour Russian Math. Surveys
\yr 2021
\vol 76
\issue 4
\pages 587--652
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Linking options:
  • https://www.mathnet.ru/eng/rm10007
  • https://doi.org/10.1070/RM10007
  • https://www.mathnet.ru/eng/rm/v76/i4/p37
    • This publication is cited in the following 7 articles:
    1. Julia Bernatska, “Abelian Function Fields on Jacobian Varieties”, Axioms, 14:2 (2025), 90  crossref
    2. Victor M. Buchstaber, Alexander V. Mikhailov, “KdV hierarchies and quantum Novikov's equations”, Open Commun. in Nonlin. Math. Physics, 2024, no. 1, 1–36  mathnet  crossref
    3. V. M. Buchstaber, E. Yu. Bunkova, “Polynomial dynamical systems associated with the KdV hierarchy”, Part. Differ. Equ. in Appl. Math., 12 (2024), 100928–6  mathnet  crossref
    4. Shigeki Matsutani, “On Real Hyperelliptic Solutions of Focusing Modified KdV Equation”, Math Phys Anal Geom, 27:4 (2024)  crossref
    5. V. M. Buchstaber, A. V. Mikhailov, “Cyclic Frobenius algebras”, Russian Math. Surveys, 78:1 (2023), 205–207  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. V. M. Buchstaber, “The Mumford dynamical system and hyperelliptic Kleinian functions”, Funct. Anal. Appl., 57:4 (2023), 288–302  mathnet  crossref  crossref  mathscinet  isi
    7. E. Yu. Bunkova, V. M. Bukhshtaber, “Parametric Korteweg–de Vries hierarchy and hyperelliptic sigma functions”, Funct. Anal. Appl., 56:3 (2022), 169–187  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:643
    Russian version PDF:175
    English version PDF:45
    Russian version HTML:277
    References:68
    First page:25
     
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