Multi-Hamiltonian structures for r-matrix systems
نویسندگان
چکیده
منابع مشابه
Generalized Hamiltonian Structures for Ermakov Systems
We construct Poisson structures for Ermakov systems, using the Er-makov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations...
متن کاملPre-hamiltonian Structures for Integrable Nonlinear Systems
Pre-Hamiltonian matrix operators in total derivatives are considered; they are defined by the property that their images are subalgebras of the Lie algebra of evolutionary vector fields. This construction is close to the Lie algebroids over infinite jet spaces. We assign a class of these operators and the brackets induced in their pre-images to integrable KdV-type hierarchies of symmetry flows ...
متن کاملOscillation Criteria for Hamiltonian Matrix Difference Systems
We obtain some oscillation criteria for the Hamiltonian difference system (AY{t) = B{t)Y{t+\) + C{t)Z{t), I AZ{t) = -A{t)Y{t + 1) B*{t)Z{t), where A, B, C, Y, Z are dxd matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.
متن کاملBäcklund Transformations for Tri-hamiltonian Dual Structures of Multi-component Integrable Systems
In this paper, the Bäcklund transformation based-approach is explored to obtain Hamiltonian operators of multi-component integrable systems which are governed by a compatible tri-Hamiltonian dual structures. The resulting Hamiltonian operators are used not only to derive multi-component biHamiltonian integrable hierarchies and their dual integrable versions, but also to serve as a criterion to ...
متن کاملBi - Hamiltonian structures for integrable systems on regular time scales
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of δ-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors is given by the use of the recursion operators of the Lax hier...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2008
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2937896