Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds”

Symmetries of Hamiltonian systems on symplectic and Poisson manifolds

On a class of nonlinear fractional Schrödinger-Poisson systems

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

On Runge-Kutta discontinuous Galerkin schemes for Vlasov-Poisson systems

In this paper we consider Runge-Kutta discontinuous Galerkin (RKDG) schemes for Vlasov-Poisson systems that model collisionless plasmas. One-dimensional systems are emphasized. The RKDG method, originally devised to solve conservation laws, is seen to have excellent conservation properties, be readily designed for arbitrary order of accuracy, and capable of being used with a positivity-preservi...

Killing-Poisson tensors on Riemannian manifolds

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the class of Poisson structures studied in (Differential Geometry and its Applications, Vol. 20, Issue 3 (2004), 279–291) and the class of Poisson structures ind...

Noncommutative Gauge Fields on Poisson Manifolds ∗

It is shown by Connes, Douglas and Schwarz that gauge theory on noncom-mutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that noncommutative gauge theories on more general manifolds also can be useful in string theory. We discuss a framework to noncommutative quantum gauge theory on Poisson manifolds by using the deformation...