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Uspekhi Mat. Nauk, 1985, Volume 40, Issue 4(244), Pages 79–89 (Mi umn2707)  

This article is cited in 37 scientific papers (total in 37 papers)

International conference "Modern Problems of Algebra and Analysis"
Plenary lectures

The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems

S. P. Novikov


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English version:
Russian Mathematical Surveys, 1985, 40:4, 85–98

Bibliographic databases:

MSC: 76Exx, 17Bxx, 34C29

Citation: S. P. Novikov, “The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems”, Uspekhi Mat. Nauk, 40:4(244) (1985), 79–89; Russian Math. Surveys, 40:4 (1985), 85–98

Citation in format AMSBIB
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\by S.~P.~Novikov
\paper The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems
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\yr 1985
\vol 40
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\pages 79--89
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\jour Russian Math. Surveys
\yr 1985
\vol 40
\issue 4
\pages 85--98
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, Theoret. and Math. Phys., 73:2 (1987), 1242–1245  mathnet  crossref  zmath  isi
    3. A. A. Balinskii, “Classification of the virasoro, the Neveu–Schwarz, and the Ramond-type simple Lie superalegrbas”, Funct. Anal. Appl., 21:4 (1987), 308–309  mathnet  crossref  mathscinet  zmath  isi
    4. O. I. Bogoyavlenskii, “The Lax representation with a spectral parameter for certain dynamical systems”, Math. USSR-Izv., 32:2 (1989), 245–268  mathnet  crossref  mathscinet  zmath
    5. O. I. Mokhov, “Dubrovin–Novikov type Poisson brackets (DN-brackets)”, Funct. Anal. Appl., 22:4 (1998), 336–338  mathnet  crossref  mathscinet  zmath
    6. L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:1 (1989), 3–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. 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
    8. B. A. Dubrovin, “Differential-geometric Poisson brackets on a lattice”, Funct. Anal. Appl., 23:2 (1989), 131–133  mathnet  crossref  mathscinet  zmath  isi
    9. 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
    10. 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
    11. 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
    12. 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
    13. 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
    14. B Dubrovin, “Integrable systems in topological field theory”, Nuclear Physics B, 379:3 (1992), 627  crossref
    15. I. M. Krichever, “The τ-function of the universal whitham hierarchy, matrix models and topological field theories”, Comm Pure Appl Math, 47:4 (1994), 437  crossref  mathscinet  zmath  isi
    16. J. Marshall Osborn, Efim Zelmanov, “Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations”, Journal of Pure and Applied Algebra, 101:3 (1995), 335  crossref
    17. Oleg I. Bogoyavlenskij, “Necessary conditions for existence of non-degenerate Hamiltonian structures”, Comm Math Phys, 182:2 (1996), 253  crossref  mathscinet  zmath  isi
    18. 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
    19. 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
    20. Maltsev A.Y., Novikov S.P., “On the local systems Hamiltonian in the weakly non-local Poisson brackets”, Physica D, 156:1–2 (2001), 53–80  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. Chengming Bai, Daoji Meng, Hongbiao Zhang, “On the central extensions of Poisson brackets of hydrodynamic type”, J Phys A Math Gen, 36:9 (2003), 2261  crossref  mathscinet  zmath  isi  elib
    22. 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
    23. 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
    24. A. Ya. Maltsev, “Whitham systems and deformations”, J Math Phys (N Y ), 47:7 (2006), 073505  crossref  mathscinet  zmath  adsnasa  isi
    25. A. Ya. Maltsev, “The Lorentz-Invariant Deformation of the Whitham System for the Nonlinear Klein–Gordon Equation”, Funct. Anal. Appl., 42:2 (2008), 103–115  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    26. Ferguson, JT, “Flat pencils of symplectic connections and Hamiltonian operators of degree 2”, Journal of Geometry and Physics, 58:4 (2008), 468  mathscinet  zmath  adsnasa  isi
    27. James T. Ferguson, “Flat pencils of symplectic connections and Hamiltonian operators of degree 2”, Journal of Geometry and Physics, 58:4 (2008), 468  crossref
    28. Ferguson, JT, “SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE Poisson BRACKETS”, Glasgow Mathematical Journal, 51A (2009), 75  crossref  mathscinet  zmath  isi
    29. 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
    30. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    31. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
    32. A. Ya. Maltsev, “The multi-dimensional Hamiltonian structures in the Whitham method”, J. Math. Phys, 54:5 (2013), 053507  crossref
    33. Ferapontov E.V., Pavlov M.V., Vitolo R.F., “Projective-Geometric Aspects of Homogeneous Third-Order Hamiltonian Operators”, J. Geom. Phys., 85 (2014), 16–28  crossref  isi
    34. A. Ya. Maltsev, “On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations”, J. Math. Phys, 56:2 (2015), 023510  crossref
    35. Ferapontov E.V. Pavlov M.V. Vitolo R.F., “Towards the Classification of Homogeneous Third-Order Hamiltonian Operators: Table 1.”, Int. Math. Res. Notices, 2016, no. 22, 6829–6855  crossref  mathscinet  isi
    36. Lorenzoni P. Savoldi A. Vitolo R., “Bi-Hamiltonian Structures of KdV Type”, J. Phys. A-Math. Theor., 51:4 (2018), 045202  crossref  isi
    37. Drensky V. Zhakhayev B.K., “Noetherianity and Specht Problem For Varieties of Bicommutative Algebras”, J. Algebra, 499 (2018), 570–582  crossref  isi
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