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

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 120, Number 2, Pages 248–255
DOI: https://doi.org/10.4213/tmf773 (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. Golubchik^a, V. V. Sokolov^b

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

Full-text PDF (192 kB) Citations (14)

References:

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

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.

Received: 25.02.1999

English version:
Theoretical and Mathematical Physics, 1999, Volume 120, Issue 2, Pages 1019–1025
DOI: https://doi.org/10.1007/BF02557409

Bibliographic databases:

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf773

https://doi.org/10.4213/tmf773

https://www.mathnet.ru/eng/tmf/v120/i2/p248

This publication is cited in the following 14 articles:

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
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.
Isaenko E.M., “O differentsialnoi geometrii obobschennogo uravneniya geizenberga”, Nauchnaya zhizn, 2011, no. 1, 29–31 On the differential geometry of generalized heisenberg equation
Aristophanes Dimakis, Folkert Müller-Hoissen, “Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions”, SIGMA, 6 (2010), 055, 27 pp.
Odesskii, AV, “Integrable matrix equations related to pairs of compatible associative algebras”, Journal of Physics A-Mathematical and General, 39:40 (2006), 12447
O. V. Efimovskaya, “Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations”, J. Math. Sci., 144:2 (2007), 3926–3937
Golubchik IZ, Sokolov VV, “Factorization of the loop algebras and compatible Lie brackets”, Journal of Nonlinear Mathematical Physics, 12 (2005), 343–350, Suppl. 1
I. Z. Golubchik, V. V. Sokolov, “Factorization of the Loop Algebra and Integrable Toplike Systems”, Theoret. and Math. Phys., 141:1 (2004), 1329–1347
Skrypnyk, T, “Deformations of loop algebras and integrable systems: hierarchies of integrable equations”, Journal of Mathematical Physics, 45:12 (2004), 4578
Sokolov, VV, “On decompositions of the loop algebra over so(3) into a sum of two subalgebras”, Doklady Mathematics, 70:1 (2004), 568
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
A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, Theoret. and Math. Phys., 127:1 (2001), 446–459
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
I. Z. Golubchik, V. V. Sokolov, “One More Kind of the Classical Yang–Baxter Equation”, Funct. Anal. Appl., 34:4 (2000), 296–298

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

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