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Dokl. Akad. Nauk SSSR, 1984, Volume 279, Number 2, Pages 294–297 (Mi dan9366)  

This article is cited in 30 scientific papers (total in 30 papers)

MATHEMATICS

Poisson brackets of hydrodynamic type

B. A. Dubrovin, S. P. Novikov

Lomonosov Moscow State University

Full text: PDF file (481 kB)

Bibliographic databases:
UDC: 513.835
Received: 20.06.1984

Citation: B. A. Dubrovin, S. P. Novikov, “Poisson brackets of hydrodynamic type”, Dokl. Akad. Nauk SSSR, 279:2 (1984), 294–297

Citation in format AMSBIB
\Bibitem{DubNov84}
\by B.~A.~Dubrovin, S.~P.~Novikov
\paper Poisson brackets of hydrodynamic type
\jour Dokl. Akad. Nauk SSSR
\yr 1984
\vol 279
\issue 2
\pages 294--297
\mathnet{http://mi.mathnet.ru/dan9366}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=770656}
\zmath{https://zbmath.org/?q=an:0591.58012}


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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. M. Polyak, “On one-dimensional Hamiltonian systems of hydrodynamic type with explicit dependence on the spatial variable”, Russian Math. Surveys, 42:3 (1987), 229–230  mathnet  crossref  mathscinet  adsnasa  isi
    3. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funct. Anal. Appl., 22:4 (1998), 336–338  mathnet  crossref  mathscinet  zmath
    4. 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
    5. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. B. A. Dubrovin, “Differential-geometric Poisson brackets on a lattice”, Funct. Anal. Appl., 23:2 (1989), 131–133  mathnet  crossref  mathscinet  zmath  isi
    7. S. P. Tsarev, “The geometry of harniltonian systems of hydrodynamic type. The generalized hodograph method”, Math. USSR-Izv., 37:2 (1991), 397–419  mathnet  crossref  mathscinet  zmath  adsnasa
    8. O. I. Mokhov, “A Hamiltonian structure of evolution in the space variable $x$ for the Korteweg–de Vries equation”, Russian Math. Surveys, 45:1 (1990), 218–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. O. I. Mokhov, “Homogeneous symplectic structures of second order on loop spaces and symplectic connections”, Funct. Anal. Appl., 25:2 (1991), 136–137  mathnet  crossref  mathscinet  zmath  isi
    10. M. V. Pavlov, “Hamiltonian formalism of multidimensional systems of hydrodynamic type having non-degenerate Lagrangian structure”, Russian Math. Surveys, 50:3 (1995), 633–634  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. A. Isaev, M. Yu. Kovalevsky, S. V. Peletminskii, “On hamiltonian approach to dynamics of continuum”, Theoret. and Math. Phys., 102:2 (1995), 208–218  mathnet  crossref  mathscinet  zmath  isi
    12. G. V. Potëmin, “On third-order Poisson brackets of differential geometry”, Russian Math. Surveys, 52:3 (1997), 617–618  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. O. I. Mokhov, “On the Cohomology Groups of Complexes of Homogeneous Forms on Loop Spaces of Smooth Manifolds”, Funct. Anal. Appl., 32:3 (1998), 162–171  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. 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
    15. A. V. Balandin, G. V. Potëmin, “On non-degenerate differential-geometric Poisson brackets of third order”, Russian Math. Surveys, 56:5 (2001), 976–977  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. O. I. Mokhov, “The classification of multidimensional Poisson brackets of hydrodynamic type”, Russian Math. Surveys, 61:2 (2006), 356–358  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. 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
    18. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib
    19. 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
    20. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    21. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
    22. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. Sara Froehlich, “The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables”, SIGMA, 14 (2018), 096, 49 pp.  mathnet  crossref
    24. M. Casati, “Higher-order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type”, Theoret. and Math. Phys., 196:2 (2018), 1129–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernoi sfery”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 78–87  mathnet  mathscinet
    26. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 110–118  mathnet  mathscinet
    27. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 119–129  mathnet  mathscinet
    28. M. V. Shamolin, “Integrable systems with many degrees of freedom and with dissipation”, Moscow University Mechanics Bulletin, 74:6 (2019), 137–146  mathnet  crossref  isi
    29. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81  mathnet  crossref
    30. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 142–156  mathnet  crossref
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