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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 27–45
DOI: https://doi.org/10.4213/faa4152
(Mi faa4152)
 

This article is cited in 2 scientific papers (total in 2 papers)

The Mumford dynamical system and hyperelliptic Kleinian functions

V. M. Buchstaber

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
References:
Abstract: We develop a differential-algebraic theory of the Mumford dynamical system. In the framework of this theory, we introduce the $(P,Q)$-recursion, which defines a sequence of functions $P_1,P_2,\ldots$ given the first function $P_1$ of this sequence and a sequence of parameters $h_1,h_2,\dots$ . The general solution of the $(P,Q)$-recursion is shown to give a solution for the parametric graded Korteweg–de Vries hierarchy. We prove that all solutions of the Mumford dynamical $g$-system are determined by the $(P,Q)$-recursion under the condition $P_{g+1} = 0$, which is equivalent to an ordinary nonlinear differential equation of order $2g$ for the function $P_1$. Reduction of the $g$-system of Mumford to the Buchstaber–Enolskii–Leykin dynamical system is described explicitly, and its explicit $2g$-parameter solution in hyperelliptic Klein functions is presented.
Keywords: Korteweg–de Vries equation, parametric KdV hierarchy, family of Poisson brackets, Gelfand–Dikii recursion, hyperelliptic Kleinian functions.
Funding agency Grant number
Russian Science Foundation 23-11-00143
Received: 14.09.2023
Revised: 14.09.2023
Accepted: 22.09.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 288–302
DOI: https://doi.org/10.1134/S0016266323040032
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Buchstaber, “The Mumford dynamical system and hyperelliptic Kleinian functions”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 27–45; Funct. Anal. Appl., 57:4 (2023), 288–302
Citation in format AMSBIB
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\by V.~M.~Buchstaber
\paper The Mumford dynamical system and hyperelliptic Kleinian functions
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 4
\pages 27--45
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\crossref{https://doi.org/10.4213/faa4152}
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\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 4
\pages 288--302
\crossref{https://doi.org/10.1134/S0016266323040032}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85189067206}
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  • https://doi.org/10.4213/faa4152
  • https://www.mathnet.ru/eng/faa/v57/i4/p27
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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