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TMF, 2004, Volume 141, Number 1, Pages 3–23 (Mi tmf113)  

This article is cited in 14 scientific papers (total in 14 papers)

Factorization of the Loop Algebra and Integrable Toplike Systems

I. Z. Golubchika, V. V. Sokolovb

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

Abstract: With any Lie algebra of Laurent series with coefficients in a semisimple Lie algebra and its decomposition into a sum of the subalgebra consisting of the Taylor series and a complementary subalgebra, we associate a hierarchy of integrable Hamiltonian nonlinear ODEs. In the case of the $so(3)$ Lie algebra, our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows generating integrable deformations for known integrable models.

Keywords: integrable nonlinear ODE, Lax pair, loop algebra

DOI: https://doi.org/10.4213/tmf113

Full text: PDF file (307 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 141:1, 1329–1347

Bibliographic databases:

Received: 12.01.2004
Revised: 04.03.2004

Citation: I. Z. Golubchik, V. V. Sokolov, “Factorization of the Loop Algebra and Integrable Toplike Systems”, TMF, 141:1 (2004), 3–23; Theoret. and Math. Phys., 141:1 (2004), 1329–1347

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Efimovskaya, “Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations”, J. Math. Sci., 144:2 (2007), 3926–3937  mathnet  crossref  mathscinet  zmath  elib
    2. S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions”, Izv. Math., 69:1 (2005), 221–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Golubchik IZ, Sokolov VV, “Factorization of the loop algebras and compatible Lie brackets”, Journal of Nonlinear Mathematical Physics, 12 (2005), 343–350, Suppl. 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and the Yang–Baxter Equation”, Theoret. and Math. Phys., 146:2 (2006), 159–169  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Dimakis A, Muller-Hoissen F, “From AKNS to derivative NLS hierarchies via deformations of associative products”, Journal of Physics A-Mathematical and General, 39:45 (2006), 14015–14033  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Odesskii AV, Sokolov VV, “Integrable matrix equations related to pairs of compatible associative algebras”, Journal of Physics A-Mathematical and General, 39:40 (2006), 12447–12456  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Sokolov VV, Wolf T, “Integrable quadratic classical Hamiltonians on so(4) and so(3,1)”, Journal of Physics A-Mathematical and General, 39:8 (2006), 1915–1926  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Odesskii AV, Sokolov VV, “Compatible Lie brackets related to elliptic curve”, Journal of Mathematical Physics, 47:1 (2006), 013506  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Odesskii A, Sokolov V, “Pairs of compatible associative algebras, classical Yang–Baxter equation and quiver representations”, Communications in Mathematical Physics, 278:1 (2008), 83–99  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Demskoi, DK, “On recursion operators for elliptic models”, Nonlinearity, 21:6 (2008), 1253  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    11. Legare M., “Samples of noncommutative products in certain differential equations”, J. Phys. A: Math. Theor., 43:44 (2010), 445208  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. R. A. Atnagulova, I. Z. Golubchik, “Novye resheniya uravneniya Yanga–Bakstera s kvadratom”, Ufimsk. matem. zhurn., 4:3 (2012), 6–16  mathnet  mathscinet
    13. A. V. Vershilov, Yu. A. Grigorev, A. V. Tsyganov, “Ob odnoi integriruemoi deformatsii volchka Kovalevskoi”, Nelineinaya dinam., 10:2 (2014), 223–236  mathnet
    14. Dobrogowska A., “R-Matrix, Lax pair, and Multiparameter Decompositions of Lie Algebras”, J. Math. Phys., 56:11 (2015), 113508  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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