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 Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 3, Pages 9–19 (Mi faa200)

Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type

I. Z. Golubchika, V. V. Sokolovb

a Bashkir State Pedagogical University
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: 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

DOI: https://doi.org/10.4213/faa200

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English version:
Functional Analysis and Its Applications, 2002, 36:3, 172–181

Bibliographic databases:

UDC: 517.958+512.81

Citation: I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 9–19; Funct. Anal. Appl., 36:3 (2002), 172–181

Citation in format AMSBIB
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• https://doi.org/10.4213/faa200
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Related articles on Google Scholar: Russian articles, English articles

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