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Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 3, Pages 16–37 (Mi faa3077)  

This article is cited in 3 scientific papers (total in 3 papers)

Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation

E. Yu. Bunkova, V. M. Buchstaber

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We consider homogeneous polynomial dynamical systems in $n$-space. To any such system our construction matches a nonlinear ordinary differential equation and an algorithm for constructing a solution of the heat equation. The classical solution given by the Gaussian function corresponds to the case $n=0$, while solutions defined by the elliptic theta-function lead to the Chazy-3 equation and correspond to the case $n=2$. We explicitly describe the family of ordinary differential equations arising in our approach and its relationship with the wide-known Darboux–Halphen quadratic dynamical systems and their generalizations.

Keywords: polynomial dynamical systems, heat equation, Chazy equation, Darboux–Halphen system

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00197_a
11-01-12067_офи_м
Ministry of Education and Science of the Russian Federation 2010-220-01-077, договор 11.G34.31.0005


DOI: https://doi.org/10.4213/faa3077

Full text: PDF file (275 kB)
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English version:
Functional Analysis and Its Applications, 2012, 46:3, 173–190

Bibliographic databases:

UDC: 517.9+517.583
Received: 11.06.2012

Citation: E. Yu. Bunkova, V. M. Buchstaber, “Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation”, Funktsional. Anal. i Prilozhen., 46:3 (2012), 16–37; Funct. Anal. Appl., 46:3 (2012), 173–190

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Yu. Netay, “Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2”, Trans. Moscow Math. Soc., 74 (2013), 281–292  mathnet  crossref  mathscinet  zmath  elib
    2. A. V. Vinogradov, “Painlevé test for ordinary differential equations associated with the heat equation”, Proc. Steklov Inst. Math., 286 (2014), 65–76  mathnet  crossref  crossref  isi  elib  elib
    3. V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • ‘ункциональный анализ и его приложени€ Functional Analysis and Its Applications
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