Geodesic
Polynomial conservation laws and exact solutions associated with isometric and homothetic symmetries in the nonlinear sigma model
Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 144-152 
G. G. Ivanov. Polynomial conservation laws and exact solutions associated with isometric and homothetic symmetries in the nonlinear sigma model. Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 144-152. http://geodesic.mathdoc.fr/item/TMF_1985_62_1_a11/
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     author = {G. G. Ivanov},
     title = {Polynomial conservation laws and exact solutions associated with isometric and homothetic symmetries in the nonlinear sigma model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {144--152},
     year = {1985},
     volume = {62},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_62_1_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the nonlinear $\sigma$ model, conserved tensor currents associated with the presence of isometric, homothetic, and affine motions in the space of values of the chiral field $V^N$ are constructed. New classes of exact solutions in the $SO(3)$- and $SO(5)$-invariant $\sigma$ models are obtained using the connection between the groups of isometric and homothetic motions of space-time and the isometric motions in $V^N$. Some methods for obtaining exact solutions in the four-dimensional $\sigma$ model with nontrivial topological charge are considered.

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