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SIGMA, 2007, Volume 3, 062, 14 pages (Mi sigma188)  

This article is cited in 5 scientific papers (total in 5 papers)

Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

Artur Sergyeyev

Mathematical Institute, Silesian University in Opava, Na Rybnícku 1, 746 01 Opava, Czech Republic

Abstract: We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure $J$ can be written as the Lie derivative of $J^{-1}$ along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamiltonian structure of zero or first order, including Hamiltonian operators of the Dubrovin–Novikov type.

Keywords: weakly nonlocal Hamiltonian structure; symplectic structure; Lie derivative

DOI: https://doi.org/10.3842/SIGMA.2007.062

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Full text: http://emis.mi.ras.ru/.../062
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Bibliographic databases:

ArXiv: math-ph/0612048
MSC: 37K10; 37K05
Received: December 15, 2006; in final form April 23, 2007; Published online April 26, 2007
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Citation: Artur Sergyeyev, “Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility”, SIGMA, 3 (2007), 062, 14 pp.

Citation in format AMSBIB
\Bibitem{Ser07}
\by Artur Sergyeyev
\paper Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
\jour SIGMA
\yr 2007
\vol 3
\papernumber 062
\totalpages 14
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\crossref{https://doi.org/10.3842/SIGMA.2007.062}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889234825}


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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. Ferguson J.T., “Flat pencils of symplectic connections and Hamiltonian operators of degree 2”, Journal of Geometry and Physics, 58:4 (2008), 468–486  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Daryoush Talati, Refik Turhan, “On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators”, SIGMA, 7 (2011), 081, 8 pp.  mathnet  crossref  mathscinet
    3. Krasil'shchik I.S., Sergyeyev A., “Integrability of S-Deformable Surfaces: Conservation Laws, Hamiltonian Structures and More”, J. Geom. Phys., 97 (2015), 266–278  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Mikhail B. Sheftel, Devrim Yazici, “Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański”, SIGMA, 12 (2016), 091, 17 pp.  mathnet  crossref
    5. Sheftel M.B. Yazici D. Malykh A.A., “Recursion operators and bi-Hamiltonian structure of the general heavenly equation”, J. Geom. Phys., 116 (2017), 124–139  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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