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Funktsional'nyi Analiz i ego Prilozheniya, 2021, Volume 55, Issue 3, Pages 3–25
DOI: https://doi.org/10.4213/faa3915
(Mi faa3915)
 

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

Hyperelliptic Sigma Functions and Adler–Moser Polynomials

V. M. Buchstaber, E. Yu. Bunkova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (706 kB) Citations (2)
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Abstract: In a 2004 paper by V. M. Buchstaber and D. V. Leykin, published in “Functional Analysis and Its Applications,” for each $g > 0$, a system of $2g$ multidimensional heat equations in a nonholonomic frame was constructed. The sigma function of the universal hyperelliptic curve of genus $g$ is a solution of this system. In our previous work, published in “Functional Analysis and Its Applications,” explicit expressions for the Schrödinger operators that define the equations of this system were obtained in the hyperelliptic case.
In this work we use these results to show that if the initial condition of the system is polynomial, then its solution is uniquely determined up to a constant factor. This has important applications in the well-known problem of series expansion for the hyperelliptic sigma function. We give an explicit description of the connection between such solutions and the well-known Burchnall–Chaundy polynomials and Adler–Moser polynomials. We find a system of linear second-order differential equations that determines the corresponding Adler–Moser polynomial.
Keywords: Schrödinger operator, polynomial Lie algebra, polynomial dynamical system, heat equation in a nonholonomic frame, differentiation of Abelian functions with respect to parameters, Adler–Moser polynomial, Burchnall–Chaundy equation, Korteweg–de Vries equation.
Received: 18.06.2021
Revised: 18.06.2021
Accepted: 21.06.2021
English version:
Functional Analysis and Its Applications, 2021, Volume 55, Issue 3, Pages 179–197
DOI: https://doi.org/10.1134/S0016266321030011
Bibliographic databases:
Document Type: Article
UDC: 515.178.2+517.958
Language: Russian
Citation: V. M. Buchstaber, E. Yu. Bunkova, “Hyperelliptic Sigma Functions and Adler–Moser Polynomials”, Funktsional. Anal. i Prilozhen., 55:3 (2021), 3–25; Funct. Anal. Appl., 55:3 (2021), 179–197
Citation in format AMSBIB
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\by V.~M.~Buchstaber, E.~Yu.~Bunkova
\paper Hyperelliptic Sigma Functions and Adler--Moser Polynomials
\jour Funktsional. Anal. i Prilozhen.
\yr 2021
\vol 55
\issue 3
\pages 3--25
\mathnet{http://mi.mathnet.ru/faa3915}
\crossref{https://doi.org/10.4213/faa3915}
\transl
\jour Funct. Anal. Appl.
\yr 2021
\vol 55
\issue 3
\pages 179--197
\crossref{https://doi.org/10.1134/S0016266321030011}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000747033300001}
Linking options:
  • https://www.mathnet.ru/eng/faa3915
  • https://doi.org/10.4213/faa3915
  • https://www.mathnet.ru/eng/faa/v55/i3/p3
  • 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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