Geodesic
Symmetries, conservation laws, and exact solutions in nonlinear sigma models
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 45-54 
G. G. Ivanov. Symmetries, conservation laws, and exact solutions in nonlinear sigma models. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 45-54. http://geodesic.mathdoc.fr/item/TMF_1983_57_1_a5/
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     author = {G. G. Ivanov},
     title = {Symmetries, conservation laws, and exact solutions in nonlinear sigma models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {45--54},
     year = {1983},
     volume = {57},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_1_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear four-dimensional $\sigma$ models interacting with the gravitational field are considered. On the basis of the connection between the groups of isometric motions of the space-time $V_4$ and the space $V_N$ of values of the chiral field exact solutions are obtained for the Einstein and chiral-field equations for spherical and plane symmetry. The conserved currents associated with the presence of the isometric motions in $V_N$ are constructed.

[1] Perelomov A. M., UFN, 134:4 (1981), 577–609 | DOI | MR

[2] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980, 319 pp. | MR

[3] Forger M., Lect. Notes Phys., 134 (1981), 110–134 | DOI | MR

[4] Din A. M., Zakrzewski W. J., Lett. Math. Phys., 5 (1981), 553–561 | DOI | MR | Zbl

[5] Ghika G., Visinescu M., Nuovo Cim., 59B:1 (1980), 59–74 | DOI | MR

[6] Petrov A. Z., Novye metody v obschei teorii otnositelnosti, Nauka, M., 1966, 495 pp. | MR

[7] Barbashov B. M., Nesterenko V. V., Commun. Math. Phys., 78 (1981), 499–506 | DOI | MR | Zbl

[8] Barbashov B. M., Nesterenko V. V., Fortschr. Phys., 28 (1980), 427–464 | DOI | MR

[9] Landau L. D., Lifshits E. M., Teoriya polya, Nauka, M., 1973, 502 pp. | MR