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

This article is cited in 82 scientific papers (total in 82 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)

Bibliographic databases:
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. M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, Theoret. and Math. Phys., 73:2 (1987), 1242–1245  mathnet  crossref  zmath  isi
    11. M. V. Pavlov, “Nonlinear Schrödinger equation and the bogolyubov-whitham method of averaging”, Theoret. and Math. Phys., 71:3 (1987), 584–588  mathnet  crossref  mathscinet  zmath  isi
    12. I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213  mathnet  crossref  mathscinet  zmath  isi
    13. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funct. Anal. Appl., 22:4 (1998), 336–338  mathnet  crossref  mathscinet  zmath
    14. B. A. Dubrovin, “Differential-geometric Poisson brackets on a lattice”, Funct. Anal. Appl., 23:2 (1989), 131–133  mathnet  crossref  mathscinet  zmath  isi
    15. 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
    16. 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
    17. O. I. Mokhov, E. V. Ferapontov, “Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature”, Russian Math. Surveys, 45:3 (1990), 218–219  mathnet  crossref  mathscinet  zmath  isi
    18. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. Funct. Anal. Appl., 24:3 (1990), 247–249  mathnet  crossref  mathscinet  zmath  isi
    20. 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
    21. 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
    22. E. V. Ferapontov, “Integration of weekly nonlinear semi-hamiltonian systems of hydrodynamic type by methods of the theory of webs”, Math. USSR-Sb., 71:1 (1992), 65–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. 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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