TY - JOUR
T1 - Classical double, R-operators, and negative flows of integrable hierarchies
JF - Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931
Y1 - 2012
A1 - Boris Dubrovin
A1 - Taras V. Skrypnyk
AB - 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.
PB - SISSA
UR - http://hdl.handle.net/1963/6468
U1 - 6413
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -