Quasi-bi-Hamiltonian systems and separability
نویسندگان
چکیده
منابع مشابه
Bi–Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
We discuss from a bi-Hamiltonian point of view the Hamilton–Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi–bi– Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton–Jacobi equation.
متن کاملQuasi-Bi-Hamiltonian Systems Obtained from Constrained Flows
The Nijenhuis tensor Φ = θ1θ −1 0 has n distinct eigenvalues μ = (μ1, . . . , μn) [3]. One can construct a canonical transformation (q, p) 7→ (μ, ν) ((μ, ν) referred to as the Nijenhuis coordinates) and the FDIHS in the Nijenhuis coordinates is separable. Several QBH systems are presented and some relationship between BH and QBH structure is discussed in [1, 2, 4, 5]. The aims of this paper is ...
متن کاملBi-Hamiltonian aspects of the separability of the Neumann system
The Neumann system on the 2-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian point of view on separation of variables. It is shown that, from this standpoint, its separation coordinates and its integrals of motion can be found in a systematic way.
متن کاملQuantum Bi-Hamiltonian Systems
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.
متن کاملOn Hamiltonian Perturbations of Hyperbolic Systems of Conservation Laws I: Quasi-Triviality of Bi-Hamiltonian Perturbations
We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs vt + [φ(v)]x = 0. Under certain genericity assumptions it is proved that any bi-Hamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on ...
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 Physics A: Mathematical and General
سال: 1997
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/30/8/023