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TMF, 2007, Volume 150, Number 2, Pages 263–285 (Mi tmf5978)  

This article is cited in 9 scientific papers (total in 9 papers)

Integrability of the Egorov systems of hydrodynamic type

M. V. Pavlov

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We present integrability criterion for the Egorov systems of hydrodynamic type. We find the general solution by the generalized hodograph method and give examples. We discuss a description of triorthogonal curvilinear coordinate systems from the standpoint of reciprocal transformations.

Keywords: Hamiltonian structure, reciprocal transformation, Egorov metric, system of hydrodynamic type, Riemann invariant, extended hodograph method, generalized hodograph method

DOI: https://doi.org/10.4213/tmf5978

Full text: PDF file (538 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 150:2, 225–243

Bibliographic databases:

Received: 01.05.2006

Citation: M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, TMF, 150:2 (2007), 263–285; Theoret. and Math. Phys., 150:2 (2007), 225–243

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. Victor D. Gershun, “Integrable String Models in Terms of Chiral Invariants of $\mathrm{SU}(n)$, $\mathrm{SO}(n)$, $\mathrm{SP}(n)$ Groups”, SIGMA, 4 (2008), 041, 16 pp.  mathnet  crossref  mathscinet  zmath
    2. V. Rosenhaus, “Infinite conservation laws for differential systems”, Theoret. and Math. Phys., 160:1 (2009), 1042–1049  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Yu-Tung Chen, Niann-Chern Lee, Ming-Hsien Tu, “The WDVV symmetries in two-primary models”, Theoret. and Math. Phys., 161:3 (2009), 1634–1646  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Sergyeyev A., “Infinite hierarchies of nonlocal symmetries of the Chen-Kontsevich-Schwarz type for the oriented associativity equations”, J. Phys. A, 42:40 (2009), 404017, 15 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. V. Neschadim, “Kasatelnye preobrazovaniya uravneniya Keli–Darbu”, Vestn. NGU. Ser. matem., mekh., inform., 9:1 (2009), 39–44  mathnet
    6. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Cirilo-Lombardo D.J., “Integrable Hydrodynamic Equations For Initial Chiral Currents and Infinite Hydrodynamic Chains From WZNW Model and String Model of WZNW Type With Su(2), So(3), Sp(2), Su(Infinity), So(Infinity), Sp(Infinity) Constant Torsions”, Int. J. Mod. Phys. A, 29:24 (2014), 1450134  crossref  zmath  adsnasa  isi  scopus
    8. Maxim V. Pavlov, “Integrability of exceptional hydrodynamic-type systems”, Proc. Steklov Inst. Math., 302 (2018), 325–335  mathnet  crossref  crossref  isi  elib
    9. Prykarpatski A.K., “On the Solutions to the Witten-Dijkgraaf-Verlinde-Verlinde Associativity Equations and Their Algebraic Properties”, J. Geom. Phys., 134 (2018), 77–83  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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