共查询到20条相似文献,搜索用时 0 毫秒
1.
研究了在欧拉-拉格朗日系统上的jet辛算法.证明了第二作者在1998年给出的一个离散的欧拉-拉格朗日(DEL)方程存在一个离散形式的几何结构,它沿着解是不变的,这个结构可以通过对离散的作用量函数求导得到.由此,可以给出此格式的jet辛性质.利用这个结构证明了与此DEL方程相关的离散Nother定理.最后,给出了一个欧拉-拉格朗日方程上的jet辛差分格式的数值算例,并与其它的差分格式进行了比较. 相似文献
2.
ZHU Jun-Yi GENG Xian-Guo 《理论物理通讯》2007,47(4):577-581
By resorting to the nonlinearization approach, a Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem is considered. A new symplectic map of the Neumann type is obtained through nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is presented, by which the symplectic reap'is further proved to be completely integrable in the Liouville sense. 相似文献
3.
By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a higher-order Bargmann symmetry constraint, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs, which we obtained are respectively nonlinearized into a new integrable symplectic map and a finite-dimensional integrable Hamiltonian system in Liouville sense. 相似文献
4.
Measure synchronization in coupled Hamiltonian systems is a novel
synchronization phenomenon. The measure synchronization on symplectic map is
observed numerically, for identical coupled systems with different
parameters. We have found the properties of the characteristic frequency and
the amplitude of phase locking in regular motion when the measure
synchronization of coupled systems is obtained. The relations between the
change of the largest Lyapunov exponent and the course of phase
desynchronization are also discussed in coupled systems, some useful results
are obtained. A new approach is proposed for describing the measure
synchronization of coupled systems numerically, which is
advantage in judging the measure synchronization, especially for the coupled
systems in nonregular region. 相似文献
5.
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable
symplectic map and finite-dimensional integrable systems are given
by nonlinearization method. The binary Bargmann constraint gives
rise to a Bäcklund transformation for the resulting
integrable lattice equations. At last, conservation laws of the
hierarchy are presented. 相似文献
6.
A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related tothis spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are givenby nonlinearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resultingintegrable lattice equations. 相似文献
7.
GUO Han-Ying LI Yu-Qi WU Ke 《理论物理通讯》2001,(7)
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler-Lagrange cohomological concepts. We also show that the trapezoidal integrator is symplectic in certain sense.`` 相似文献
8.
Izu Vaisman 《Journal of Geometry and Physics》1986,3(4):507-524
The paper describes the geometry of the bundle
(M, ω) of the compatible complex structures of the tangent spaces of an (almost) symplectic manifold (M, ω), from the viewpoint of general twistor spaces [3], [9], [1]. It is shown that M has an either complex or almost Kaehler twistor space iff it has a flat symplectic connection. Applications of the twistor space
to the study of the differential forms of M, and to the study of mappings : N → M, where N is a Kaehler manifold are indicated. 相似文献
9.
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the
noncommutative differential calculus with respect to the discrete time
and the Euler-Lagrange cohomological concepts. We also show that the trapezoidal integrator is symplectic in certain sense. 相似文献
10.
By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-Kähler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show that any special symplectic connection can be constructed using symplectic realizations of quadratic deformations of a certain linear Poisson structure. Moreover, we show that these Poisson structures cannot be symplectically integrated by a Hausdorff groupoid. As a consequence, we obtain a canonical principal line bundle over any special symplectic manifold or orbifold, and we deduce numerous global consequences. 相似文献
11.
By applying the Fourier slice theorem, Sθ(λ) =∫^∞-∞Pθ(t)e^-iλt=F(λcosθ,λsinθ),where Pθ(t) is a projection of f(x,p)=^∞∫∫-∞F(u,v)e^i(uz+up) dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator (pure state), which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation. 相似文献
12.
A universal symplectic structure for a Newtonian system including
nonconservative cases can be constructed in the framework of Birkhoffian
generalization of Hamiltonian mechanics. In this paper the symplectic
geometry structure of Birkhoffian system is discussed, then the
symplecticity of Birkhoffian phase flow is presented. Based on these
properties we give a way to construct symplectic schemes for Birkhoffian
systems by using the generating function method. 相似文献
13.
By applying the Fourier slice theorem, Sθ(λ) =∫_{-\infty }^{\infty }Pθ(t)e-iλt=F(λcosθ,λsinθ), where Pθ(t) is a projection of f( x,p) =∫∫_{-\infty}^{\infty }F( u,v) ei(ux+vp)ldudv along lines of constant, to the Wigner operator we are naturally led to projection operator (pure state), which results in a new complete epresentation. The Weyl orderimg formalism of the Wigner operator is used in the derivation. 相似文献
14.
Brandon Carter 《International Journal of Theoretical Physics》2003,42(6):1317-1327
This paper treats the generalization to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developed by Witten, Zuckerman, and others in the context of field theory. After a general presentation, including a review of the relationships between the various (Lagrangian, Eulerian, and other) relevant kinds of variation, the procedure is illustrated by application to the particularly simple case of branes of the Dirac—Goto—Nambu type, in which internal fields are absent. 相似文献
15.
The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger (DNLS) equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established. 相似文献
16.
WANG ShunJin &ZHANG Hua Center of Theoretical Physics Sichuan University Chengdu China 《中国科学G辑(英文版)》2007,50(2):133-143
Based on the algebraic dynamics solution of ordinary differential equations andintegration of ,the symplectic algebraic dynamics algorithm sn is designed,which preserves the local symplectic geometric structure of a Hamiltonian systemand possesses the same precision of the na ve algebraic dynamics algorithm n.Computer experiments for the 4th order algorithms are made for five test modelsand the numerical results are compared with the conventional symplectic geometric algorithm,indicating that sn has higher precision,the algorithm-inducedphase shift of the conventional symplectic geometric algorithm can be reduced,and the dynamical fidelity can be improved by one order of magnitude. 相似文献
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19.
We find that with uniform mesh, the numerical schemes derived
from finite element method can keep a preserved symplectic structure
in one-dimensional case and a preserved multisymplectic structure in
two-dimensional case respectively.
These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice. 相似文献