Geodesic
Variational Poisson–Nijenhuis structures for partial differential
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 268-282 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : Poisson–Nijenhuis structure, nonlocal structure.
Keywords: symmetry, conservation law, covering 
@article{TMF_2008_154_2_a5,
     author = {V. A. Golovko and I. S. Krasil'shchik and A. M. Verbovetsky},
     title = {Variational {Poisson{\textendash}Nijenhuis} structures for partial differential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {268--282},
     year = {2008},
     volume = {154},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a5/}
}
TY  - JOUR
AU  - V. A. Golovko
AU  - I. S. Krasil'shchik
AU  - A. M. Verbovetsky
TI  - Variational Poisson–Nijenhuis structures for partial differential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 268
EP  - 282
VL  - 154
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a5/
LA  - ru
ID  - TMF_2008_154_2_a5
ER  - 
%0 Journal Article
%A V. A. Golovko
%A I. S. Krasil'shchik
%A A. M. Verbovetsky
%T Variational Poisson–Nijenhuis structures for partial differential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 268-282
%V 154
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a5/
%G ru
%F TMF_2008_154_2_a5
V. A. Golovko; I. S. Krasil'shchik; A. M. Verbovetsky. Variational Poisson–Nijenhuis structures for partial differential. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 268-282. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a5/

[1] I. Vaisman, “A lecture on Poisson–Nijenhuis structures,”, Integrable Systems and Foliations (Feuilletages et systèmes intégrables) (Montpellier, 1995), Progr. Math., 145, Birkhäuser Boston, Boston, MA, 1997, 169–185 | MR | Zbl

[2] J. V. Beltrán, J. Monterde, Ann. Global Anal. Geom., 12:1 (1994), 65–78 | DOI | MR | Zbl

[3] Y. Kosmann-Schwarzbach, Lett. Math. Phys., 38:4 (1996), 421–428 | DOI | MR | Zbl

[4] Y. Kosmann-Schwarzbach, F. Magri, Ann. Inst. H. Poincaré, 53:1 (1990), 35–81 | MR | Zbl

[5] F. Magri, C. Morosi, A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson–Nijenhuis manifolds, Quaderno 19, University of Milan, 1984

[6] P. Kersten, I. Krasil'shchik, A. Verbovetsky, J. Geom. Phys., 50:1–4 (2004), 273–302 ; arXiv: math.DG/0304245 | DOI | MR | Zbl

[7] P. H. M. Kersten, I. S. Krasil'shchik, A. M. Verbovetsky, Acta Appl. Math., 90:1–2 (2006), 143–178 ; arXiv: nlin.SI/0511012 | DOI | MR | Zbl

[8] I. S. Krasil'shchik, Differential Geom. Appl., 2:4 (1992), 307–350 | DOI | MR | Zbl

[9] A. M. Vinogradov, “Cohomological Analysis of Partial Differential Equations and Secondary Calculus”, Transl. Math. Monogr., 204, American Mathematical Society, Providence, RI, 2001 | MR | Zbl

[10] A. Cabras, A. M. Vinogradov, J. Geom. Phys., 9:1 (1992), 75–100 | DOI | MR | Zbl

[11] A. V. Bocharov, A. M. Verbovetskii, A. M. Vinogradov i dr., Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, eds. A. M. Vinogradov, I. S. Krasilschik, Faktorial-press, M., 2005

[12] P. Kersten, I. Krasil'shchik, A. Verbovetsky, Acta Appl. Math., 83:1–2 (2004), 167–173 ; arXiv: math.DG/0310451 | DOI | MR | Zbl

[13] I. S. Krasil'shchik, A. M. Vinogradov, Acta Appl. Math., 15:1–2 (1989), 161–209 | DOI | MR | Zbl

[14] P. J. Olver, J. Sanders, J. P. Wang, J. Nonlinear Math. Phys., 9 (2002), 164–172, Suppl. 1 | DOI | MR

[15] N. G. Khorkova, Tr. MGTU, 1988, no. 512, 105–119

[16] A. M. Verbovetskii, V. A. Golovko, I. S. Krasilschik, Nauchn. vestn. MGTUGA. Ser. Matematika, fizika, 91 (2007), 13–21

[17] N. H. Ibragimov, J. Math. Anal. Appl., 333:1 (2007), 311–328 | DOI | MR | Zbl