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Uspekhi Mat. Nauk, 1985, Volume 40, Issue 4(244), Pages 217–218 (Mi umn2755)  

This article is cited in 20 scientific papers (total in 20 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

On Poisson brackets of hydrodynamic type with a degenerate metric

N. I. Grinberg


Full text: PDF file (228 kB)
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English version:
Russian Mathematical Surveys, 1985, 40:4, 231–232

Bibliographic databases:

MSC: 15A21, 15A18, 15A72, 15A57, 15A03
Received: 15.05.1984

Citation: N. I. Grinberg, “On Poisson brackets of hydrodynamic type with a degenerate metric”, Uspekhi Mat. Nauk, 40:4(244) (1985), 217–218; Russian Math. Surveys, 40:4 (1985), 231–232

Citation in format AMSBIB
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\by N.~I.~Grinberg
\paper On Poisson brackets of hydrodynamic type with a~degenerate metric
\jour Uspekhi Mat. Nauk
\yr 1985
\vol 40
\issue 4(244)
\pages 217--218
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\zmath{https://zbmath.org/?q=an:0611.58017}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1985RuMaS..40R.231G}
\transl
\jour Russian Math. Surveys
\yr 1985
\vol 40
\issue 4
\pages 231--232
\crossref{https://doi.org/10.1070/RM1985v040n04ABEH003662}
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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. S. P. Novikov, “The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems”, Russian Math. Surveys, 40:4 (1985), 85–98  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    3. A. Ya. Mal'tsev, “The averaging of local field-theoretic Poisson brackets”, Russian Math. Surveys, 52:2 (1997), 409–411  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. I. A. B. Strachan, “Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations”, J Math Phys (N Y ), 40:10 (1999), 5058  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. Ya. Maltsev, “Conservation of Hamiltonian structures in Whitham's averaging method”, Izv. Math., 63:6 (1999), 1171–1201  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. I. A. Strachan, “Degenerate bi-Hamiltonian structures of the hydrodynamic type”, Theoret. and Math. Phys., 122:2 (2000), 247–255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A Ya Maltsev, “Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type”, J Phys A Math Gen, 38:3 (2005), 637  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Błażej M. Szablikowski, Maciej Błaszak, “Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems”, J Math Phys (N Y ), 47:9 (2006), 092701  crossref  mathscinet  zmath  adsnasa  isi
    10. Maxim V. Pavlov, “Hydrodynamic chains and the classification of their Poisson brackets”, J Math Phys (N Y ), 47:12 (2006), 123514  crossref  mathscinet  zmath  isi
    11. Oleg I. Bogoyavlenskij, “Tensor Invariants of the Poisson Brackets of Hydrodynamic Type”, Comm Math Phys, 277:2 (2007), 369  crossref  mathscinet  isi
    12. Oleg I. Bogoyavlenskij, “Invariant foliations for the Poisson brackets of hydrodynamic type”, Physics Letters A, 360:4-5 (2007), 539  crossref  elib
    13. Oleg I. Bogoyavlenskij, “Invariant dynamical system for a Poisson bracket of hydrodynamic type”, Physics Letters A, 365:1-2 (2007), 105  crossref  elib
    14. O. Bogoyavlenskij, P. Reynolds, “Form-invariant Poisson brackets of hydrodynamic type with several spatial variables”, J Math Phys (N Y ), 49:5 (2008), 053520  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. O. I. Mokhov, “The Classification of Nonsingular Multidimensional Dubrovin–Novikov Brackets”, Funct. Anal. Appl., 42:1 (2008), 33–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. A Ya Maltsev, “The conservation of the Hamiltonian structures in the deformations of the Whitham systems”, J Phys A Math Theor, 43:6 (2010), 065202  crossref  mathscinet  zmath  adsnasa  elib
    17. Bogoyavlenskij O.I., Reynolds A.P., “Criteria for Existence of a Hamiltonian Structure”, Regular & Chaotic Dynamics, 15:4–5 (2010), 431–439  crossref  isi
    18. I.A.. B. Strachan, Błaże.M.. Szablikowski, “Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations”, Studies in Applied Mathematics, 2014, n/a  crossref
    19. Andrea Savoldi, “Degenerate first-order Hamiltonian operators of hydrodynamic type in 2D”, J. Phys. A: Math. Theor, 48:26 (2015), 265202  crossref
    20. Savoldi A., “On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric”, J. Geom. Phys., 104 (2016), 246–276  crossref  mathscinet  zmath  isi  elib  scopus
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