Geodesic
Systems of equations of $n$-waves and nonlinear Schrödinger equations from the group-theoretical point of view
Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 3, pp. 405-413 
A. V. Zhiber. Systems of equations of $n$-waves and nonlinear Schrödinger equations from the group-theoretical point of view. Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 3, pp. 405-413. http://geodesic.mathdoc.fr/item/TMF_1982_52_3_a6/
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     author = {A. V. Zhiber},
     title = {Systems of equations of $n$-waves and nonlinear {Schr\"odinger} equations from the group-theoretical point of view},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {1982},
     volume = {52},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_52_3_a6/}
}
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The paper is devoted to group-theoretical analysis of a system of equations of $n$-waves and a system of nonlinear Schrödinger equations. The Lie–Bäcklund algebras of these equations are fully described. These algebras are commutative, and there is a one-toone correspondence between them and the commutative Lie algebras of the conservation laws. The connection between the Lie–Bäcklund algebras of the considered systems of equations is found.

[1] Ibragimov N. Kh., Matem. sbornik, 109 (1979), 229–253 | MR | Zbl

[2] Zakharov V. E., Manakov S. V., ZhETF, 69:5 (1975), 1651–1673

[3] Manakov S. V., O tochnom reshenii sistemy nelineinykh uravnenii Shredingera, Preprint IYaF 26-73, IYaF, Novosibirsk, 1973

[4] Zhiber A. V., Funkts. analiz i ego prilozh., 11:1 (1977), 65–66 | MR | Zbl

[5] Lax P. D., Comm. Pure Appl. Math., 21 (1968), 467–490 | DOI | MR | Zbl

[6] Zhiber A. V., Smirnova N. D., Integriruemye sistemy, Ufa, 1982, 31–40

[7] Ibragimov N. Kh., Shabat A. B., Funkts. analiz i ego prilozh., 14:1 (1980), 25–36 | MR | Zbl