Using the classical double G of a Lie algebra gequipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie-Poisson bracket on g* and its extensions. We consider examples of Lie algebras g with the "Adler-Kostant-Symes" R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U-V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. © 2012 Pleiades Publishing, Ltd.

Dubrovin, B., Skrypnyk, T. (2012). Classical double, R-operators, and negative flows of integrable hierarchies. THEORETICAL AND MATHEMATICAL PHYSICS, 172(1), 911-931 [10.1007/s11232-012-0086-6].

Classical double, R-operators, and negative flows of integrable hierarchies

SKRYPNYK, TARAS
2012

Abstract

Using the classical double G of a Lie algebra gequipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie-Poisson bracket on g* and its extensions. We consider examples of Lie algebras g with the "Adler-Kostant-Symes" R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U-V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. © 2012 Pleiades Publishing, Ltd.
Articolo in rivista - Articolo scientifico
classical R-operator; integrable hierarchy; Mathematical Physics; Statistical and Nonlinear Physics
English
2012
172
1
911
931
none
Dubrovin, B., Skrypnyk, T. (2012). Classical double, R-operators, and negative flows of integrable hierarchies. THEORETICAL AND MATHEMATICAL PHYSICS, 172(1), 911-931 [10.1007/s11232-012-0086-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/66828
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