共查询到20条相似文献,搜索用时 31 毫秒
1.
The multisymplectic geometry for the Zakharov–Kuznetsov equation is presented in this Letter. The multisymplectic form and the local energy and momentum conservation laws are derived directly from the variational principle. Based on the multisymplectic Hamiltonian formulation, we derive a 36-point multisymplectic integrator. 相似文献
2.
Total Variation and Multisymplectic Structure for CNLS System 总被引:1,自引:0,他引:1
SUN Jian-Qiang QIN Meng-Zhao LIU Ting-Ting 《理论物理通讯》2006,46(1):28-32
The relation between the toal variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schroedinger system are obtained directly from the variational principle. 相似文献
3.
A multisymplectic formulation for the Zakhaxov system is presented. The semi-explicit multisymplectic integrator of the formulation is constructed by means of the Euier-box scheme. Numerical results on simulating the propagation of one soliton and the collision of two solitons axe reported to illustrate the efficiency of the multisymplectic scheme. 相似文献
4.
The relation between the total variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schrodinger system are obtained directly from the variational principle. 相似文献
5.
6.
CHEN Jing-Bo 《理论物理通讯》2004,41(4):561-566
The multisymplectic geometry for
the seismic wave equation is presented in this paper. The local
energy conservation law, the local momentum evolution equations, and
the multisymplectic form are derived directly from the
variational principle. Based on the covariant Legendre transform,
the multisymplectic Hamiltonian formulation is developed.
Multisymplectic discretization and numerical experiments are also
explored. 相似文献
7.
Jerrold E. Marsden Sergey Pekarsky Steve Shkoller Matthew West 《Journal of Geometry and Physics》2001,38(3-4)
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper. 相似文献
8.
9.
10.
Multisymplectic structures for one-way wave equations are presented in this letter. Based on the multisymplectic formulation,
we obtain the corresponding multisymplectic discretizations. The structure-preserving property of a finite difference scheme
for the first-order one-way wave equation is proved. Implications and applications of this result are explored.
相似文献
11.
In the paper, we describe a novel kind of multisymplectic method for three-dimensional (3-D) Maxwell’s equations. Splitting the 3-D Maxwell’s equations into three local one-dimensional (LOD) equations, then applying a pair of symplectic Runge–Kutta methods to discretize each resulting LOD equation, it leads to splitting multisymplectic integrators. We say this kind of schemes to be LOD multisymplectic scheme (LOD-MS). The discrete conservation laws, convergence, dispersive relation, dissipation and stability are investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, non-dissipative, and of first order accuracy in time and second order accuracy in space. As a reduction, we also consider the application of LOD-MS to 2-D Maxwell’s equations. Numerical experiments match the theoretical results well. They illustrate that LOD-MS is not only efficient and simple in coding, but also has almost all the nature of multisymplectic integrators. 相似文献
12.
Multisymplectic Geometry and Its Appiications for the Schrodinger Equation in Quantum Mechanics
下载免费PDF全文
![点击此处可从《中国物理快报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Multisymplectic geometry for the Schrodinger equation in quantum mechanics is presented. This formalism of multisymplectic geometry provides a concise and complete introduction to the Schrodinger equation. The Schrodinger equation, its associated energy and momentum evolution equations, and the multisymplectic form are derived directly from the variational principle. Some applications are also explored. 相似文献
13.
Jing-Bo Chen 《Letters in Mathematical Physics》2006,75(3):293-305
We present symplectic and multisymplectic formulations of the Klein-Gordon equation in this paper. Based on these two formulations,
we investigate the corresponding symplectic and multisymplectic Fourier pseudospectral discretizations. The relationship between
these two kinds of Fourier pseudospectral discretizations is discussed. Time discretizations are also presented. 相似文献
14.
A variational formulation for the multisymplectic Hamiltonian systems is presented in this Letter. Using this variational formulation, we obtain multisymplectic integrators from a variational perspective. Numerical experiments are also reported.Mathematical Subject Classifications (2000). 70G50, 58Z05. 相似文献
15.
In the previous papers I and II,we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach.We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the lagrangian and Hamiltonian formalisms.In this paper,we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms.We will show that either Hamiltonian schemes of Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied. 相似文献
16.
A total variation calculus in discrete multisymplectic field theory is developed in this Letter. Using this discrete total variation calculus, we obtain multisymplectic-energy-momentum integrators. The multisymplectic discretization for the nonlinear Schrödinger equation is also presented. 相似文献
17.
18.
We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration. 相似文献
19.
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively.We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire grometric object and the noncommutative differential calculus on regular lattice.In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations,the Euler-Lagrange cohomological concepts and content in the configuration space are employed. 相似文献
20.
A multisymplectic variational internal energy corresponding equation, its associated local framework for the nonlinear elastic wave equation is presented. The modified to the approximate nonlinea.r elastic wave equation is derived, we obtain the energy and momentum conservation laws as well as the multisymplectic form simultaneously directly from the variational principle 相似文献