Related papers: Nambu mechanics viewed as a Clebsch parameterized …
The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV…
In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system. We found in two simplest cases the complete sets of the integrals of motion using Nambu--Poisson…
We present a variational principle for relativistic hydrodynamics with gauge-anomaly terms for a fluid coupled to an Abelian background gauge field. For this we utilize the Clebsch parametrization of the velocity field. We also set up the…
Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…
We investigate Hamiltonian fluid reductions of the one-dimensional Vlasov-Poisson equation. Our approach utilizes the hydrodynamic Poisson bracket framework, which allows us to systematically identify fundamental normal variables derived…
Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new…
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu's generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the…
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations, using the conservation for energy and potential enstrophy, is presented. Different mechanisms, such as vortical flows and emission of gravity…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
We consider n-linear Nambu brackets in dimension N higher than n. Starting from a Hamiltonian system with a Poisson bracket and K Casimir invariants defined in the phase space of dimension N = K+2M, where M is the number of effective…
The globalization problem arises when local tensor fields possess a given property (such as being symplectic or Poisson) but cannot be consistently extended to a global object due to incompatibilities on chart overlaps. A notable instance…
We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For…
We briefly discuss the Hamiltonian formalism of Kantowski-Sachs space-times with vacuum, anisotropic fluid and two cross-streaming radiation field sources. For these models a cosmological time is introduced. New constraints are found in…
An extension of the Liouville-von Neumann dynamics to a Nambu-type dynamics is proposed. The resulting theory is the first version of nonlinear QM which is free from internal inconsistencies.