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TMF, 2008, Volume 154, Number 2, Pages 268–282 (Mi tmf6168)  

This article is cited in 8 scientific papers (total in 8 papers)

Variational Poisson–Nijenhuis structures for partial differential equations

V. A. Golovkoa, I. S. Krasil'shchikb, A. M. Verbovetskyb

a M. V. Lomonosov Moscow State University
b Independent University of Moscow

Abstract: We explore variational Poisson–Nijenhuis structures on nonlinear partial differential equations and establish relations between the Schouten and Nijenhuis brackets on the initial equation and the Lie bracket of symmetries on its natural extensions (coverings). This approach allows constructing a framework for the theory of nonlocal structures.

Keywords: Poisson–Nijenhuis structure, symmetry, conservation law, covering, nonlocal structure

DOI: https://doi.org/10.4213/tmf6168

Full text: PDF file (483 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 154:2, 227–239

Bibliographic databases:

Received: 01.05.2007

Citation: V. A. Golovko, I. S. Krasil'shchik, A. M. Verbovetsky, “Variational Poisson–Nijenhuis structures for partial differential equations”, TMF, 154:2 (2008), 268–282; Theoret. and Math. Phys., 154:2 (2008), 227–239

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v154/i2/p268

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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. Golovko V., Kersten P., Krasil'shchik I., Verbovetsky A., “On integrability of the Camassa-Holm equation and its invariants”, Acta Appl. Math., 101:1-3 (2008), 59–83  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kiselev A.V., van de Leur J.W., “A family of second Lie algebra structures for symmetries of a dispersionless Boussinesq system”, J. Phys. A, 42:40 (2009), 404011, 8 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    3. Hussin V., Kiselev A.V., Krutov A. ., Wolf T., “$N=2$ supersymmetric $a=4$-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation”, J. Math. Phys., 51:8 (2010), 083507, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. A. V. Kiselev, J. W. van de Leur, “Variational Lie algebroids and homological evolutionary vector fields”, Theoret. and Math. Phys., 167:3 (2011), 772–784  mathnet  crossref  crossref  adsnasa  isi
    5. Krasil'shchik J., Verbovetsky A., “Geometry of jet spaces and integrable systems”, J. Geom. Phys., 61:9 (2011), 1633–1674  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Kiselev A.V., “Homological Evolutionary Vector Fields in Korteweg-de Vries, Liouville, Maxwell, and Several Other Models”, 7th International Conference on Quantum Theory and Symmetries (QTS7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012058  crossref  isi  scopus
    7. Krasil'shchik I.S., Verbovetsky A.M., Vitolo R., “A Unified Approach to Computation of Integrable Structures”, Acta Appl. Math., 120:1 (2012), 199–218  crossref  mathscinet  zmath  isi  scopus
    8. Kiselev A.V., Krutov A.O., “Non-Abelian Lie Algebroids Over Jet Spaces”, J. Nonlinear Math. Phys., 21:2 (2014), 188–213  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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