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This article is cited in 6 scientific papers (total in 6 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
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.
Received: 10.05.2021
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
Linking options:
https://www.mathnet.ru/eng/rm10007https://doi.org/10.1070/RM10007 https://www.mathnet.ru/eng/rm/v76/i4/p37
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Abstract page: | 565 | Russian version PDF: | 151 | English version PDF: | 33 | Russian version HTML: | 222 | References: | 56 | First page: | 24 |
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