Geodesic
Lie–Poisson structures over differential algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 3, pp. 459-472 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Based on key elements of Olver's approach to partial differential equations for Hamiltonian evolution, we propose an algebraic construction appropriate for Hamiltonian evolutionary systems with constraints.
Keywords: differential algebra, differential bicomplex, Hamiltonian map, Hamiltonian evolution system of partial differential equations
Mots-clés : Lie–Poisson structure, constraint. 
@article{TMF_2017_192_3_a4,
     author = {V. V. Zharinov},
     title = {Lie{\textendash}Poisson structures over differential algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {459--472},
     year = {2017},
     volume = {192},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a4/}
}
TY  - JOUR
AU  - V. V. Zharinov
TI  - Lie–Poisson structures over differential algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 459
EP  - 472
VL  - 192
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a4/
LA  - ru
ID  - TMF_2017_192_3_a4
ER  - 
%0 Journal Article
%A V. V. Zharinov
%T Lie–Poisson structures over differential algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 459-472
%V 192
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a4/
%G ru
%F TMF_2017_192_3_a4
V. V. Zharinov. Lie–Poisson structures over differential algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 3, pp. 459-472. http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a4/

[1] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | DOI | MR | MR | Zbl | Zbl

[2] V. V. Zharinov, “Formalnyi kompleks de Rama”, TMF, 174:2 (2013), 256–271 | DOI | DOI | MR | Zbl

[3] V. V. Zharinov, “Operational calculus in differential algebras”, Integral Transform. Spec. Funct., 7:1–2 (1998), 145–158 | DOI | MR | Zbl

[4] V. V. Zharinov, “Zakony sokhraneniya evolyutsionnykh sistem”, TMF, 68:2 (1986), 163–171 | DOI | MR | Zbl

[5] V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations, Series on Soviet and East European Mathematics, 9, World Sci., Singapore, 1992 | MR | Zbl

[6] V. V. Zharinov, “Evolyutsionnye sistemy so svyazyami v vide uslovii nulevoi divergentsii”, TMF, 163:1 (2010), 3–16 | DOI | DOI | Zbl

[7] V. V. Zharinov, “O preobrazovanii Beklunda”, TMF, 189:3 (2016), 323–334 | DOI | DOI | MR

[8] A. Sergeev, “The Sobolev space of half-differentiable functions and quasisymmetric homeomorphisms”, Georgian Math. J., 23:4 (2016), 615–622 | DOI | MR | Zbl

[9] A. G. Sergeev, “Kvantovoe ischislenie i kvazikonformnye otobrazheniya”, Matem. zametki, 100:1 (2016), 144–154 | DOI | DOI | MR | Zbl

[10] M. O. Katanaev, “Rotational elastic waves in a cylindrical waveguide with wedge dislocation”, J. Phys. A: Math. Theor., 49:8 (2016), 085202, 8 pp. | DOI | MR | Zbl

[11] M. O. Katanaev, “Vektornye polya Killinga i odnorodnaya i izotropnaya vselennaya”, UFN, 186:7 (2016), 763–775 | DOI | DOI

[12] N. G. Marchuk, D. S. Shirokov, “Constant solutions of Yang–Mills equations and generalized Proca equations”, J. Geom. Symmetry Phys., 42 (2016), 53–72, arXiv: 1611.03070 | MR | Zbl

[13] A. K. Guschin, “$L_p$-otsenki nekasatelnoi maksimalnoi funktsii dlya resheniya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 207:10 (2016), 28–55 | DOI | DOI | MR

[14] A. K. Pogrebkov, “Kommutatornye tozhdestva na assotsiativnykh algebrakh, raznostnoe neabelevo uravnenie Khiroty i ego reduktsii”, TMF, 187:3 (2016), 433–446 | DOI | DOI | MR

[15] D. V. Bykov, “Tsiklicheskie graduirovki algebr Li i pary Laksa dlya sigma-modelei”, TMF, 189:3 (2016), 380–388 | DOI | DOI | MR

[16] A. A. Slavnov, “Kvantovanie modelei massivnykh neabelevykh kalibrovochnykh polei so spontanno narushennoi simmetriei vne ramok teorii vozmuschenii”, TMF, 189:2 (2016), 279–285 | DOI | DOI | Zbl