Related papers: Phase Flows and Vector Hamiltonians
A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered.…
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V.Arnold, as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. In this…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…
We consider the Kepler potential and its relatives $q\mapsto -\|q\|^{-2(1-1/n)}$, $n\in\mathbb{N}$ in arbitrary dimension $d$. We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete…
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…
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…
We employ Monte Carlo simulations to study a generalized three-dimensional complex $psi|^4 theory of Ginzburg-Landau form and compare our numerical results with a recent quasi-analytical mean-field type approximation, which predicts…
We obtain the full hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated hamiltonian functionals and the corresponding Poisson structures follow from…
We show that the De Donder-Weyl (DW) covariant Hamiltonian field equations of any field can be written in Duffin-Kemmer-Petiau (DKP) matrix form. As a consequence, the (modified) DKP beta-matrices (5 X 5 in four space-time dimensions) are…
We define a super Nambu-Poisson algebra over a super manifold. A super Nambu bracket does not satisfy the usual skew-symmetric property, and we propose another skew-symmetric property. We show that the divergence of super Nambu-Hamiltonian…
The necessary number of commuting vector fields for the Chaplygin ball in the absolute space is constructed. We propose to get these vector fields in framework of the Poisson geometry similar to the Hamiltonian mechanics.
In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra,…
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
We are developing a new method for the analysis of queuing systems with heterogeneous in time and space compound (marked) Poisson input flow. The state space of the input flow is embedded in a higher-dimensional space with a homogeneous…
This paper develops a unified framework for observables in n-plectic geometry, extending the L_infty-algebra of Hamiltonian (n-1)-forms to Hamiltonian forms of all degrees via a degree-shifting Grassmann variable u that encodes submanifold…
We present a new parametrisation of the space of solutions of the Wess-Zumino-Witten model on a cylinder, with target space a compact, connected Lie group G. Using the covariant canonical approach the phase space of the theory is shown to…
We generalize the notion of weight for Gelfan'd-Fuks cohomology theory of symplectic vector spaces to the homogeneous Poisson vector spaces, and try some combinatorial approach to Poisson cohomology groups.
Some paradoxical aspects of the Nos\'e and Nos\'e-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible,…