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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 4, Pages 13–26 (Mi faa165)  

This article is cited in 7 scientific papers (total in 7 papers)

Egorov Hydrodynamic Chains, the Chazy Equation, and $SL(2,\mathbb{C})$

V. M. Buchstabera, D. V. Leikinb, M. V. Pavlovc

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Magnetism, National Academy of Sciences of Ukraine
c Loughborough University

Abstract: The general solution of the system of differential equations describing Egorov hydrodynamic chains is constructed. The solution is given in terms of the elliptic sigma function. Invariants of the sigma function are expressed as differential polynomials in a solution of the Chazy equation. The orbits of the induced action of $SL(2,\mathbb{C})$ and degenerating operators in the space of solutions are described.

Keywords: hydrodynamic chain, Egorov type system, Chazy equation, elliptic function, $SL(2)$

DOI: https://doi.org/10.4213/faa165

Full text: PDF file (191 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:4, 251–262

Bibliographic databases:

Document Type: Article
UDC: 514.7
Received: 15.09.2003

Citation: V. M. Buchstaber, D. V. Leikin, M. V. Pavlov, “Egorov Hydrodynamic Chains, the Chazy Equation, and $SL(2,\mathbb{C})$”, Funktsional. Anal. i Prilozhen., 37:4 (2003), 13–26; Funct. Anal. Appl., 37:4 (2003), 251–262

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Ferapontov, K. R. Khusnutdinova, M. V. Pavlov, “Classification of Integrable $(2+1)$-Dimensional Quasilinear Hierarchies”, Theoret. and Math. Phys., 144:1 (2005), 907–915  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Ferapontov, EV, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Mathematische Annalen, 339:1 (2007), 61  crossref  mathscinet  zmath  isi  elib  scopus
    3. E. Yu. Bunkova, V. M. Buchstaber, “Heat Equations and Families of Two-Dimensional Sigma Functions”, Proc. Steklov Inst. Math., 266 (2009), 1–28  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Buchstaber V.M., “Heat Equations and Sigma Functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 46–58  crossref  adsnasa  isi  scopus
    5. E. Yu. Bunkova, V. M. Buchstaber, “Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation”, Funct. Anal. Appl., 46:3 (2012), 173–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Brezhnev Yu.V., “Non-Canonical Extension of Theta-Functions and Modular Integrability of Theta-Constants”, Proc. R. Soc. Edinb. Sect. A-Math., 143:4 (2013), 689–738  crossref  mathscinet  zmath  isi  scopus
    7. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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