Geodesic
Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 9-19.

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We consider two classes of integrable nonlinear hyperbolic systems on Lie algebras. These systems generalize the principal chiral model. Each system is related to a pair of compatible Lie brackets and has a Lax representation, which is determined by the direct sum decomposition of the Lie algebra of Laurent series into the subalgebra of Taylor series and the complementary subalgebra corresponding to the pair. New examples of compatible Lie brackets are given.
Keywords: compatible Lie brackets; principal chiral model; homogeneous subalgebras. 
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I. Z. Golubchik; V. V. Sokolov. Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 9-19. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a1/

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