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

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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 4, Pages 13–26
DOI: https://doi.org/10.4213/faa165 (Mi faa165)

This article is cited in 11 scientific papers (total in 11 papers)

Egorov Hydrodynamic Chains, the Chazy Equation, and

$SL(2,\mathbb{C})$

V. M. Buchstaber^a, D. V. Leikin^b, M. V. Pavlov^c

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

Full-text PDF (191 kB) Citations (11)

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

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,

$SL(2)$ .

Received: 15.09.2003

English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 4, Pages 251–262
DOI: https://doi.org/10.1023/B:FAIA.0000015576.05085.bc

Bibliographic databases:

Document Type: Article

UDC: 514.7

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/faa165

https://doi.org/10.4213/faa165

https://www.mathnet.ru/eng/faa/v37/i4/p13

This publication is cited in the following 11 articles:

Ferapontov E.V., Pavlov M.V., Xue L., “Second-Order Integrable Lagrangians and Wdvv Equations”, Lett. Math. Phys., 111:2 (2021), 58
Clery F., Ferapontov V E., “Dispersionless Hirota Equations and the Genus 3 Hyperelliptic Divisor”, Commun. Math. Phys., 376:2 (2020), 1397–1412
I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
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
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
Evgeny Vladimirovich Ferapontov, Lenos Hadjikos, Karima Robertovna Khusnutdinova, “Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian”, International Mathematics Research Notices, 2010:3 (2010), 496
E. Yu. Bunkova, V. M. Buchstaber, “Heat Equations and Families of Two-Dimensional Sigma Functions”, Proc. Steklov Inst. Math., 266 (2009), 1–28
Buchstaber V.M., “Heat Equations and Sigma Functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 46–58
Ferapontov, EV, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Mathematische Annalen, 339:1 (2007), 61
Michael Trott, The Mathematica GuideBook for Numerics, 2006, 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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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