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

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 2, Pages 268–282
DOI: https://doi.org/10.4213/tmf6168 (Mi tmf6168)

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

Variational Poisson–Nijenhuis structures for partial differential equations

V. A. Golovko^a, I. S. Krasil'shchik^b, A. M. Verbovetsky^b

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

Full-text PDF (483 kB) Citations (8)

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

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.

Received: 01.05.2007

English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 2, Pages 227–239
DOI: https://doi.org/10.1007/s11232-008-0022-y

Bibliographic databases:

Language: Russian

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

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https://doi.org/10.4213/tmf6168

https://www.mathnet.ru/eng/tmf/v154/i2/p268

This publication is cited in the following 8 articles:

Kiselev A.V., Krutov A.O., “Non-Abelian Lie Algebroids Over Jet Spaces”, J. Nonlinear Math. Phys., 21:2 (2014), 188–213
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
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
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
Krasil'shchik J., Verbovetsky A., “Geometry of jet spaces and integrable systems”, J. Geom. Phys., 61:9 (2011), 1633–1674
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.
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.
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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