%0 Journal Article
%J Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931
%D 2012
%T Classical double, R-operators, and negative flows of integrable hierarchies
%A Boris Dubrovin
%A Taras V. Skrypnyk
%X Using the classical double G of a Lie algebra g equipped 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.
%B Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931
%I SISSA
%G en
%U http://hdl.handle.net/1963/6468
%1 6413
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-11T14:56:54Z (GMT) No. of bitstreams: 0
%R 10.1007/s11232-012-0086-6