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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
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We show how to construct discrete Maxwell equations by discrete exterior calculus. The new scheme has many virtues compared to the traditional Yee's scheme: it is a multisymplectic scheme and keeps geometric properties. Moreover, it can be applied on triangular mesh and thus is more adaptive to handle domains with irregular shapes. We have implemented this scheme on a Java platform successfully and our experimental results show that this scheme works well. 相似文献
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We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Nu- merical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations. 相似文献
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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
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Multisymplectic Geometry and Its Appiications for the Schrodinger Equation in Quantum Mechanics 下载免费PDF全文
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
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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
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In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure. 相似文献
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BAIYong-Qiang LIUZhen PEIMing ZHENGZhu-Jun 《理论物理通讯》2003,40(1):1-8
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure. 相似文献
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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
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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
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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
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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
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We explore the multisymplectic Fourier pseudospectral discretizations for the (3+1)-dimensional Klein-Gordon equation in this paper. The corresponding multisymplectic conservation laws are derived. Two kinds of explicit
symplectic integrators in time are also presented. 相似文献
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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
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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
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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