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 TMF, 1997, Volume 112, Number 3, Pages 375–383 (Mi tmf1049)

Integrable equations on $\mathbb Z$-graded Lie algebras

I. Z. Golubchik, V. V. Sokolov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Evolution systems with $L$$A$-pairs in $\mathbb Z$-graded Lie algebras are investigated. Some different hierarchies of integrable systems are associated with the same $L$-operator. They correspond to different decompositions of zero component of the $\mathbb Z$-graded algebra in a direct sum of two subalgebras. As the result, new examples of multi-component integrable systems are constructed.

DOI: https://doi.org/10.4213/tmf1049

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English version:
Theoretical and Mathematical Physics, 1997, 112:3, 1097–1103

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Citation: I. Z. Golubchik, V. V. Sokolov, “Integrable equations on $\mathbb Z$-graded Lie algebras”, TMF, 112:3 (1997), 375–383; Theoret. and Math. Phys., 112:3 (1997), 1097–1103

Citation in format AMSBIB
\Bibitem{GolSok97} \by I.~Z.~Golubchik, V.~V.~Sokolov \paper Integrable equations on $\mathbb Z$-graded Lie algebras \jour TMF \yr 1997 \vol 112 \issue 3 \pages 375--383 \mathnet{http://mi.mathnet.ru/tmf1049} \crossref{https://doi.org/10.4213/tmf1049} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1486795} \zmath{https://zbmath.org/?q=an:0968.35524} \elib{http://elibrary.ru/item.asp?id=13250921} \transl \jour Theoret. and Math. Phys. \yr 1997 \vol 112 \issue 3 \pages 1097--1103 \crossref{https://doi.org/10.1007/BF02583041} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000071403900002} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. Z. Golubchik, V. V. Sokolov, “Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 120:2 (1999), 1019–1025
2. Gurses, M, “On construction of recursion operators from Lax representation”, Journal of Mathematical Physics, 40:12 (1999), 6473
3. A. V. Gladkov, V. V. Dmitrieva, R. A. Sharipov, “Some nonlinear equations reducible to diffusion-type equations”, Theoret. and Math. Phys., 123:1 (2000), 436–445
4. 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
5. I. Z. Golubchik, V. V. Sokolov, “One More Kind of the Classical Yang–Baxter Equation”, Funct. Anal. Appl., 34:4 (2000), 296–298
6. A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, Theoret. and Math. Phys., 127:1 (2001), 446–459
7. Sokolov, VV, “On decompositions of the loop algebra over so(3) into a sum of two subalgebras”, Doklady Mathematics, 70:1 (2004), 568
8. 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.
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