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TMF, 1999, Volume 120, Number 2, Pages 248–255 (Mi tmf773)  

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

Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras

I. Z. Golubchika, V. V. Sokolovb

a Bashkir State Pedagogical University
b Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: We study the integrable systems of the Heisenberg equation type that correspond to different decompositions of $\mathbb Z$-graded Lie algebras into a direct sum of two subalgebras. We discover new non-Abelian generalizations of some known integrable models.

DOI: https://doi.org/10.4213/tmf773

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English version:
Theoretical and Mathematical Physics, 1999, 120:2, 1019–1025

Bibliographic databases:

Received: 25.02.1999

Citation: I. Z. Golubchik, V. V. Sokolov, “Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras”, TMF, 120:2 (1999), 248–255; Theoret. and Math. Phys., 120:2 (1999), 1019–1025

Citation in format AMSBIB
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\paper Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras
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\vol 120
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\pages 248--255
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\crossref{https://doi.org/10.4213/tmf773}
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\zmath{https://zbmath.org/?q=an:0999.37050}
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 2
\pages 1019--1025
\crossref{https://doi.org/10.1007/BF02557409}
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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. I. Z. Golubchik, V. V. Sokolov, “Multicomponent generalization of the hierarchy of the Landau–Lifshitz equation”, Theoret. and Math. Phys., 124:1 (2000), 909–917  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. I. Z. Golubchik, V. V. Sokolov, “One More Kind of the Classical Yang–Baxter Equation”, Funct. Anal. Appl., 34:4 (2000), 296–298  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, Theoret. and Math. Phys., 127:1 (2001), 446–459  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type”, Funct. Anal. Appl., 36:3 (2002), 172–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. Z. Golubchik, V. V. Sokolov, “Factorization of the Loop Algebra and Integrable Toplike Systems”, Theoret. and Math. Phys., 141:1 (2004), 1329–1347  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Skrypnyk, T, “Deformations of loop algebras and integrable systems: hierarchies of integrable equations”, Journal of Mathematical Physics, 45:12 (2004), 4578  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Sokolov, VV, “On decompositions of the loop algebra over so(3) into a sum of two subalgebras”, Doklady Mathematics, 70:1 (2004), 568  mathscinet  zmath  isi
    8. 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
    9. 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  scopus
    10. Odesskii, AV, “Integrable matrix equations related to pairs of compatible associative algebras”, Journal of Physics A-Mathematical and General, 39:40 (2006), 12447  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. Aristophanes Dimakis, Folkert Müller-Hoissen, “Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions”, SIGMA, 6 (2010), 055, 27 pp.  mathnet  crossref  mathscinet
    12. Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov, Tihomir I. Valchev, “Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces”, SIGMA, 7 (2011), 096, 48 pp.  mathnet  crossref  mathscinet
    13. Isaenko E.M., “O differentsialnoi geometrii obobschennogo uravneniya geizenberga”, Nauchnaya zhizn, 2011, no. 1, 29–31  elib
    14. Fritzsche B., Kaashoek M.A., Kirstein B., Sakhnovich A.L., “Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations”, Math. Nachr., 289:14-15 (2016), 1792–1819  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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