Quasi-Bi-Hamiltonian Systems Obtained from Constrained Flows

Quasi-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 ...

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.

Quantum 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.

On 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 ...

Steady Vortex Flows Obtained from a Constrained Variational Problem