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Decompositions of the loop algebra over so(4) and integrable models of the chiral equation type

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Abstract

Decompositions of the loop algebra over so(4) are considered and the exactly integrable nonlinear hyperbolic systems of the principal chiral field equation type are analyzed. A new example of such a system is found and the Lax representation for this example is constructed.

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References

  1. I. Z. Golubchik and V. V. Sokolov, “One more instance of the classical Yang-Baxter equation,” in: Funkts. Anal. Prilozh., 34, No. 4, 75–78 (2000).

    MathSciNet  Google Scholar 

  2. I. Z. Golubchik and V. V. Sokolov, “Compatible Lie brackets and integrable equations of the type of the principal chiral field model,” in: Funkts. Anal. Prilozh., 36, No. 3, 9–19 (2002).

    MathSciNet  Google Scholar 

  3. I. V. Cherednik, “On the integrability of the two-dimensional asymmetric chiral O(3)-field and its quantum analogue,” Yad. Fiz., 33, 278–282 (1981).

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  4. V. V. Sokolov, “On the decompositions of the loop algebra over so(3) to a sum of two subalgebras,” Dokl. Ross. Akad. Nauk (to appear).

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Authors and Affiliations

  1. Moscow State University, Russia

    O. V. Efimovskaya

  2. Landau Institute for Theoretical Physics, Moscow

    V. V. Sokolov

Authors
  1. O. V. Efimovskaya
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  2. V. V. Sokolov
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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.

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Efimovskaya, O.V., Sokolov, V.V. Decompositions of the loop algebra over so(4) and integrable models of the chiral equation type. J Math Sci 136, 4385–4391 (2006). https://doi.org/10.1007/s10958-006-0231-6

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  • DOI: https://doi.org/10.1007/s10958-006-0231-6

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