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Funktsional. Anal. i Prilozhen., 1988, Volume 22, Issue 4, Pages 92–93 (Mi faa1164)  

This article is cited in 21 scientific papers (total in 21 papers)

Brief communications

Dubrovin–Novikov type Poisson brackets (DN-brackets)

O. I. Mokhov


Full text: PDF file (206 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 1998, 22:4, 336–338

Bibliographic databases:

UDC: 513.835
Received: 13.05.1987

Citation: O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funktsional. Anal. i Prilozhen., 22:4 (1988), 92–93; Funct. Anal. Appl., 22:4 (1998), 336–338

Citation in format AMSBIB
\Bibitem{Mok88}
\by O.~I.~Mokhov
\paper Dubrovin--Novikov type Poisson brackets (DN-brackets)
\jour Funktsional. Anal. i Prilozhen.
\yr 1988
\vol 22
\issue 4
\pages 92--93
\mathnet{http://mi.mathnet.ru/faa1164}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=977008}
\zmath{https://zbmath.org/?q=an:0671.58006}
\transl
\jour Funct. Anal. Appl.
\yr 1998
\vol 22
\issue 4
\pages 336--338
\crossref{https://doi.org/10.1007/BF01077434}


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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. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, Theoret. and Math. Phys., 136:1 (2003), 908–916  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. 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
    8. 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
    9. Ferapontov E.V., Odesskii A.V., Stoilov N.M., “Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions”, J Math Phys, 52:7 (2011), 073505  crossref  isi
    10. Ferapontov E.V. Novikov V.S. Stoilov N.M., “Dispersive Deformations of Hamiltonian Systems of Hydrodynamic Type in 2+1 Dimensions”, Physica D, 241:23-24 (2012), 2138–2144  crossref  isi
    11. Maltsev A.Ya., “The Multi-Dimensional Hamiltonian Structures in the Whitham Method”, J. Math. Phys., 54:5 (2013), 053507  crossref  isi
    12. Pavlov M.V., “Hamiltonian Formalism of Two-Dimensional Vlasov Kinetic Equation”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2172 (2014), 20140343  crossref  isi
    13. Casati M., “On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type”, Commun. Math. Phys., 335:2 (2015), 851–894  crossref  isi
    14. Ferapontov E.V. Lorenzoni P. Savoldi A., “Hamiltonian Operators of Dubrovin-Novikov Type in 2D”, Lett. Math. Phys., 105:3 (2015), 341–377  crossref  isi
    15. Savoldi A., “Degenerate First-Order Hamiltonian Operators of Hydrodynamic Type in 2D”, J. Phys. A-Math. Theor., 48:26 (2015), 265202  crossref  isi
    16. Maltsev A.Ya., “On the canonical forms of the multi-dimensional averaged Poisson brackets”, J. Math. Phys., 57:5 (2016), 053501  crossref  mathscinet  zmath  isi  elib  scopus
    17. Carlet G. Casati M. Shadrin S., “Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets”, J. Geom. Phys., 114 (2017), 404–419  crossref  mathscinet  zmath  isi  scopus
    18. Qinxiu Sun, Fang Li, “A generalization of Lie $H$-pseudo-bialgebras”, Theoret. and Math. Phys., 192:1 (2017), 939–957  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    19. 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
    20. Carlet G. Casati M. Shadrin S., “Normal Forms of Dispersive Scalar Poisson Brackets With Two Independent Variables”, Lett. Math. Phys., 108:10 (2018), 2229–2253  crossref  isi
    21. 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  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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