This article is cited in 10 papers

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

T. V. Skrypnik<sup>ab

a</sup> 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: 10.4213/tmf1786

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

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