A trace identity is proposed and it is shown that this identity can be effectively applied to establish the Hamiltonian structure of the KP, DS hierarchies and a new hierarchy of ( 1 -I-2)dimensional systems.1900
The algebraic structure of the gradient-holonomic algorithm for Lax integrable dynamical systems is discussed. A generalization of the ℛ-structure approach for the case of operator-valued affine Lie algebras is used to prove the bi-Hamiltonian formulation of nonlinear integrable dynamical systems in multidimensions. The monodromy transfer matrix is constructed to describe the operator manifold in relation to canonical Lie–Poisson bracket on initial affine Lie algebra with gauge central extension. As an illustration, the two-dimensional operator Benney–Kaup integrable hierarchy is considered and their bi-Hamiltonicity is proved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.