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TMF, 2005, Volume 142, Number 2, Pages 329–345 (Mi tmf1786)  

This article is cited in 9 scientific papers (total in 9 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

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

DOI: https://doi.org/10.4213/tmf1786

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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 275–288

Bibliographic databases:


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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    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. 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
    2. Taras V. Skrypnyk, “Quasigraded Lie Algebras and Modified Toda Field Equations”, SIGMA, 2 (2006), 043, 14 pp.  mathnet  crossref  mathscinet  zmath
    3. Skrypnyk T, “Special quasigraded Lie algebras and integrable Hamiltonian systems”, Acta Applicandae Mathematicae, 99:3 (2007), 261–282  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. T. V. Skrypnik, “Dual $R$-matrix integrability”, Theoret. and Math. Phys., 155:1 (2008), 633–645  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Taras V. Skrypnik, “Classical $R$-Operators and Integrable Generalizations of Thirring Equations”, SIGMA, 4 (2008), 011, 19 pp.  mathnet  crossref  mathscinet  zmath
    6. B. A. Dubrovin, T. V. Skrypnik, “Classical double, $R$-operators, and negative flows of integrable hierarchies”, Theoret. and Math. Phys., 172:1 (2012), 911–931  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    7. Skrypnyk T., “Infinite-Dimensional Lie Algebras, Classical R-Matrices, and Lax Operators: Two Approaches”, J. Math. Phys., 54:10 (2013), 103507  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Skrypnyk T., ““Many-Poled” R-Matrix Lie Algebras, Lax Operators, and Integrable Systems”, J. Math. Phys., 55:8 (2014), 083507  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Skrypnyk T., “Reduction in Soliton Hierarchies and Special Points of Classical R-Matrices”, J. Geom. Phys., 130 (2018), 260–287  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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