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Journal of Mathematical Sciences

, Volume 136, Issue 6, pp 4385–4391 | Cite as

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

  • O. V. Efimovskaya
  • V. V. Sokolov
Article
  • 13 Downloads

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.

Keywords

Taylor Series Integrable Model Commutation Relation Hyperbolic System Loop Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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).MathSciNetGoogle Scholar
  2. 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).MathSciNetGoogle Scholar
  3. 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).Google Scholar
  4. 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).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • O. V. Efimovskaya
    • 1
  • V. V. Sokolov
    • 2
  1. 1.Moscow State UniversityRussia
  2. 2.Landau Institute for Theoretical PhysicsMoscow

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