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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 6, Pages 117–146 (Mi izv269)  

This article is cited in 9 scientific papers (total in 9 papers)

Conservation of Hamiltonian structures in Whitham's averaging method

A. Ya. Maltsev

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: In this paper we consider Whitham's averaging method for systems with a local field-theoretic Hamiltonian structure. We prove that such a Hamiltonian structure is conserved in the process. The study is based on the procedure (suggested by Dubrovin and Novikov) of averaging the local Poisson bracket, for which we establish the necessary properties of conservation of the Jacobi identity and invariance.

DOI: https://doi.org/10.4213/im269

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English version:
Izvestiya: Mathematics, 1999, 63:6, 1171–1201

Bibliographic databases:

MSC: 58F05
Received: 27.08.1997

Citation: A. Ya. Maltsev, “Conservation of Hamiltonian structures in Whitham's averaging method”, Izv. RAN. Ser. Mat., 63:6 (1999), 117–146; Izv. Math., 63:6 (1999), 1171–1201

Citation in format AMSBIB
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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. O. I. Mokhov, “Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations”, Proc. Steklov Inst. Math., 225 (1999), 269–284  mathnet  mathscinet  zmath
    2. 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  scopus
    3. 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  scopus
    4. Liu S.Q., Zhang Y.J., “Deformations of semisimple bihamiltonian structures of hydrodynamic type”, Journal of Geometry and Physics, 54:4 (2005), 427–453  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. A. Ya. Maltsev, “Whitham systems and deformations”, J Math Phys (N Y ), 47:7 (2006), 073505  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. 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  isi  elib  scopus
    7. V. L. Vereshchagin, “Single-Phase Averaging for the Ablowitz–Ladik Chain”, Math. Notes, 87:6 (2010), 797–806  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
    9. 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  mathscinet  zmath  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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