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Quasigraded Lie algebras, Kostant-Adler scheme, and integrable hierarchies. (English) Zbl 1178.37092
Theor. Math. Phys. 142, No. 2, 275-288 (2005); translation from Teor. Mat. Fiz. 142, No. 2, 329-345 (2005).
Summary: 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.
MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
17B80 Applications of Lie algebras and superalgebras to integrable systems
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