Quasi-Bi-Hamiltonian Systems Obtained from Constrained Flows
نویسنده
چکیده
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 to show how to construct an infinite number of families of QBH systems from the constrained flows of soliton equations [6–10] and to prove that the Nijenhuis coordinates for the underlying families of QBH systems are exactly the same as the separated variables introduced by the Lax matrices [11–13].
منابع مشابه
v 1 1 0 N ov 1 99 8 ON A CLASS OF DYNAMICAL SYSTEMS BOTH QUASI - BI - HAMILTONIAN AND BI - HAMILTONIAN
It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero in [1]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained trough a non canonical map whose form is directly suggested by the associated Nijenhuis tensor.
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