Geodesic
Decompositions of the loop algebra over $\mathrm{so}(4)$ and integrable models of the chiral equation type
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 39-47.

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Decompositions of the loop algebra over $\mathrm{so}(4)$ are considered and the exactly integrable nonlinear hyperbolic systems of the principal chiral field equation type are analyzed. New example of such system is found and the Lax representation for this example is constructed. 
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O. V. Efimovskaya; V. V. Sokolov. Decompositions of the loop algebra over $\mathrm{so}(4)$ and integrable models of the chiral equation type. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 39-47. http://geodesic.mathdoc.fr/item/FPM_2004_10_1_a4/

[1] Golubchik I. Z., Sokolov V. V., “Esche odna raznovidnost klassicheskogo uravneniya Yanga–Bakstera”, Funktsion. analiz i ego pril., 34:4 (2000), 75–78 | MR | Zbl

[2] Golubchik I. Z., Sokolov V. V., “Soglasovannye skobki Li i integriruemye uravneniya tipa modeli glavnogo kiralnogo polya”, Funktsion. analiz i ego pril., 36:3 (2002), 9–19 | MR | Zbl

[3] Sokolov V. V., “O razlozheniyakh algebry petel nad $\mathrm{so}(3)$ v summu dvukh podalgebr”, Dokl. RAN (to appear)

[4] Cherednik I. V., “Ob integriruemosti dvumernogo asimmetrichnogo kiralnogo LB $O(3)$-polya i ego kvantovogo analoga”, Yadernaya fizika, 33 (1981), 278–282