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Dokl. Akad. Nauk SSSR, 1983, Volume 270, Number 4, Pages 781–785 (Mi dan46101)  

This article is cited in 58 scientific papers (total in 58 papers)

MATHEMATICS

Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov–Whitman averaging method

B. A. Dubrovin, S. P. Novikov

Landau Institute for Theoretical Physics, USSR Academy of Sciences, Chernogolovka Moscow region

Full text: PDF file (653 kB)

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UDC: 513.835
Received: 04.02.1983

Citation: B. A. Dubrovin, S. P. Novikov, “Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov–Whitman averaging method”, Dokl. Akad. Nauk SSSR, 270:4 (1983), 781–785

Citation in format AMSBIB
\Bibitem{DubNov83}
\by B.~A.~Dubrovin, S.~P.~Novikov
\paper Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov--Whitman averaging method
\jour Dokl. Akad. Nauk SSSR
\yr 1983
\vol 270
\issue 4
\pages 781--785
\mathnet{http://mi.mathnet.ru/dan46101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0715332}
\zmath{https://zbmath.org/?q=an:0553.35011}


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    1. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. P. Tsarev, “On the Liouville Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov–Whitham averaging theory”, Russian Math. Surveys, 39:6 (1984), 227–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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
    4. N. I. Grinberg, “On Poisson brackets of hydrodynamic type with a degenerate metric”, Russian Math. Surveys, 40:4 (1985), 231–232  mathnet  crossref  zmath  adsnasa  isi
    5. O. I. Mokhov, “Local third-order Poisson brackets”, Russian Math. Surveys, 40:5 (1985), 233–234  mathnet  crossref  mathscinet  zmath  adsnasa
    6. Yu. L. Daletskii, “Hamiltonian operators in graded formal calculus of variations”, Funct. Anal. Appl., 20:2 (1986), 136–138  mathnet  crossref  mathscinet  zmath  isi
    7. M. B. Sheftel, “Integration of Hamiltonian systems of hydrodynamic type with two dependent variables with the aid of the Lie–Bäcklund group”, Funct. Anal. Appl., 20:3 (1986), 227–235  mathnet  crossref  mathscinet  zmath  isi
    8. O. I. Mokhov, “Hamiltonian differential operators and contact geometry”, Funct. Anal. Appl., 21:3 (1987), 217–223  mathnet  crossref  mathscinet  zmath  isi
    9. 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
    10. I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213  mathnet  crossref  mathscinet  zmath  isi
    11. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funct. Anal. Appl., 22:4 (1998), 336–338  mathnet  crossref  mathscinet  zmath
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    14. 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
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    18. B. A. Dubrovin, “Differential geometry of strongly integrable systems of hydrodynamic type”, Funct. Anal. Appl., 24:4 (1990), 280–285  mathnet  crossref  mathscinet  zmath  isi
    19. 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
    20. E. V. Ferapontov, “Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type”, Funct. Anal. Appl., 25:3 (1991), 195–204  mathnet  crossref  mathscinet  zmath  isi
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    24. M. V. Pavlov, “Discrete symmetry and local Hamiltonian structures of systems of hydrodynamical type”, Russian Math. Surveys, 48:6 (1993), 178–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    26. V. L. Alekseev, “On non-local Hamiltonian operators of hydrodynamic type connected with Whitham's equations”, Russian Math. Surveys, 50:6 (1995), 1253–1255  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. M. V. Pavlov, “Conservation of the ‘forms’ of Hamiltonian structures upon linear substitution for independent variables”, Math. Notes, 57:5 (1995), 489–495  mathnet  crossref  mathscinet  zmath  isi  elib
    28. A. Ya. Maltsev, M. V. Pavlov, “On Whitham's Averaging Method”, Funct. Anal. Appl., 29:1 (1995), 6–19  mathnet  crossref  mathscinet  zmath  isi
    29. I. M. Krichever, “Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations”, Funct. Anal. Appl., 31:1 (1997), 25–39  mathnet  crossref  crossref  mathscinet  zmath  isi
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