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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 17–26
DOI: https://doi.org/10.4213/faa4153 (Mi faa4153) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The mumford dynamical system and the Gelfand–Dikii recursion

P. G. Baron

University of Chicago
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DOI: https://doi.org/10.4213/faa4153
Abstract: In his paper “The Mumford dynamical system and hyperelliptic Kleinian functions” [Funkts. Anal. Prilozhen. 57 (4), 27–45 (2023)] Victor Buchstaber developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the $(P,Q)$-recursion introduced in his paper.
In the present paper, we further develop the theory of the $(P,Q)$-recursion and describe its connections to the Korteweg–de Vries hierarchy, the Lenard operator, and the Gelfand–Dikii recursion.
Keywords: Korteweg–de Vries (KdV) equation, parametric KdV hierarchy, Gelfand–Dikii hierarchy, Lenard operator, polynomial dynamical systems, polynomial integrals, differential polynomials.
Received: 12.09.2023
Revised: 12.09.2023
Accepted: 25.09.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 279–287
DOI: https://doi.org/10.1134/S0016266323040020
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. G. Baron, “The mumford dynamical system and the Gelfand–Dikii recursion”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 17–26; Funct. Anal. Appl., 57:4 (2023), 279–287
Citation in format AMSBIB
\Bibitem{Bar23}
\by P.~G.~Baron
\paper The mumford dynamical system and the Gelfand--Dikii recursion
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 4
\pages 17--26
\mathnet{http://mi.mathnet.ru/faa4153}
\crossref{https://doi.org/10.4213/faa4153}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 4
\pages 279--287
\crossref{https://doi.org/10.1134/S0016266323040020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185870588}
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  • https://www.mathnet.ru/eng/faa/v57/i4/p17
    • 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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    Full-text PDF :5
    References:26
    First page:13
     
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