Geodesic
Group structure and the basis of conservation laws
Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 2, pp. 244-251 
R. S. Khamitova. Group structure and the basis of conservation laws. Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 2, pp. 244-251. http://geodesic.mathdoc.fr/item/TMF_1982_52_2_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The derivation of conservation laws for invariant variational problems is based on Noether's identity. It is shown that this identity also makes it possible to establish a connection between a basis of conservation laws (with respect to the group $G$ admitted by the considered system of differential equations) and the structure of the Lie algebra of $G$. This provides a justifieation for the basis construction scheme proposed by Ibragimov.

[1] Ibragimov N. Kh., Dinamika sploshnoi sredy, no. 38, Novosibirsk, 1979, 26 | MR

[2] Anderson R. L., Ibragimov N. H., Lie-Bäcklund Transformations in Applications, SIAM, Philadelphia, 1979 | MR

[3] Ibragimov N. Kh., Matem. sb., 109:2 (1979), 229 | MR | Zbl

[4] Noether E., “Invariante Variationsprobleme”, Göttingen Nachrichten, math.-phys. Kl., 2 (1918), 235

[5] Ibragimov N. Kh., TMF, 1:3 (1969), 350–359 | MR

[6] Kucharchyk P., Teoria grup Liego w zastosowaniu do równán rózniczkowych cza̧stkowych, IPPT PAN, Warszawa, 1967

[7] Sukhinin S. V., Dinamika sploshnoi sredy, no. 36, Novosibirsk, 1978, 130 | MR

[8] Khamitova R. S., DAN SSSR, 248:4 (1979), 798–801 | MR