Geodesic
Clebsch transformation of hydrodynamic equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 1, pp. 77-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A geometric meaning of the Clebsch transformation of the hydrodynamic equations for an ideal fluid is established, as well as its relation to the reduction of differential 1-forms to the Darboux normal form. The corresponding kinematic conservation laws are described. The well-known conservation law for the number of quasiparticles is considered as a particular example. 
@article{TMF_1998_115_1_a4,
     author = {A. I. Yaremchuk},
     title = {Clebsch transformation of hydrodynamic equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {77--84},
     year = {1998},
     volume = {115},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_115_1_a4/}
}
TY  - JOUR
AU  - A. I. Yaremchuk
TI  - Clebsch transformation of hydrodynamic equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 77
EP  - 84
VL  - 115
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_115_1_a4/
LA  - ru
ID  - TMF_1998_115_1_a4
ER  - 
%0 Journal Article
%A A. I. Yaremchuk
%T Clebsch transformation of hydrodynamic equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 77-84
%V 115
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1998_115_1_a4/
%G ru
%F TMF_1998_115_1_a4
A. I. Yaremchuk. Clebsch transformation of hydrodynamic equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 1, pp. 77-84. http://geodesic.mathdoc.fr/item/TMF_1998_115_1_a4/

[1] A. Clebsch, Crelle's J. (J. für die reine und angewandte Mathematik), LIV (1857) ; LVI (1859) | Zbl

[2] H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge, 1924 | MR | Zbl

[3] E. A. Kuznetsov, A. V. Mikhailov, Physica D, 2 (1981), 224–243 | DOI

[4] G. Falkovich, V. S. L'vov, Chaos, Solitons and Fractals, 5 (1995), 1855–1865 | DOI

[5] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR | Zbl

[6] L. D. Landau, E. M. Lifshits, Gidrodinamika, Nauka, M., 1986 | MR

[7] V. E. Zakharov, Izv. vuzov. Radiofizika, 17 (1974), 431–453

[8] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya: metody i prilozheniya, T. 1, Nauka, M., 1979 | MR

[9] S. P. Novikov, Sov. Sci. Rev., 91 (1986), 1

[10] V. I. Arnold, A. B. Givental, “Simplekticheskaya geometriya”, Itogi nauki i tekhniki. Ser. Sovremennye probl. matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 8–140

[11] V. E. Zakharov, V. S. Lvov, Izv. vuzov. Radiofizika, 18 (1975), 1470