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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 142, Number 2, Pages 329–345
DOI: https://doi.org/10.4213/tmf1786 (Mi tmf1786) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Quasigraded lie algebras, Kostant–Adler scheme, and integrable hierarchies

T. V. Skrypnikab

a N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
b Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (316 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf1786
Abstract: Using special “anisotropic” quasigraded Lie algebras, we obtain a number of new hierarchies of integrable nonlinear equations in partial derivatives admitting zero-curvature representations. Among them are an anisotropic deformation of the Heisenberg magnet hierarchy, a matrix and vector generalization of the Landau–Lifshitz hierarchies, new types of matrix and vector anisotropic chiral-field hierarchies, and other types of anisotropic hierarchies.
Keywords: hierarchies of integrable models, infinite algebras, Kostant–Adler scheme.
English version:
Theoretical and Mathematical Physics, 2005, Volume 142, Issue 2, Pages 275–288
DOI: https://doi.org/10.1007/s11232-005-0072-3
Bibliographic databases:
Language: Russian
Citation: T. V. Skrypnik, “Quasigraded lie algebras, Kostant–Adler scheme, and integrable hierarchies”, TMF, 142:2 (2005), 329–345; Theoret. and Math. Phys., 142:2 (2005), 275–288
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v142/i2/p329
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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