@article {2012,
title = {Classical double, R-operators, and negative flows of integrable hierarchies},
journal = {Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931},
year = {2012},
publisher = {SISSA},
abstract = {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{\textendash}Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the {\textquotedblleft}Adler{\textendash}Kostant{\textendash}Symes{\textquotedblright} 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{\textendash}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.},
doi = {10.1007/s11232-012-0086-6},
url = {http://hdl.handle.net/1963/6468},
author = {Boris Dubrovin and Taras V. Skrypnyk}
}