共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation u
tt
− c(u)(c(u)u
x
)
x
=0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values. 相似文献
3.
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs 总被引:14,自引:0,他引:14
Jerrold E. Marsden George W. Patrick Steve Shkoller 《Communications in Mathematical Physics》1998,199(2):351-395
4.
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
5.
Eric Paturel 《Communications in Mathematical Physics》2000,213(2):249-266
In this paper, we prove the existence of infinitely many solutions of a stationary nonlinear Dirac equation on the Schwarzschild
metric, outside a massive ball. These solutions are the critical points of a strongly indefinite functional. Thanks to a concavity
property, we are able to construct a reduced functional, which is no longer strongly indefinite. We find critical points of
this new functional using the Symmetric Mountain Pass Lemma. Note that, as A. Bachelot-Motet conjectured, these solutions
vanish as the radius of the massive ball tends to the horizon radius of the metric.
Received: 2 August 1999 / Accepted: 14 February 2000 相似文献
6.
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
7.
8.
In this paper we prove a new variational principle for the Navier-Stokes equation which asserts that its solutions are critical points of a stochastic control problem in the group of area-preserving diffeomorphisms. This principle is a natural extension of the results by Arnold, Ebin, and Marsden concerning the Euler equation.Supported in part by FCT/POCTI/FEDER 相似文献
9.
10.
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
11.
12.
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
13.
Ashfaque H. Bokhari A. H. Kara M. Karim F. D. Zaman 《International Journal of Theoretical Physics》2009,48(7):1919-1928
In this paper we discuss symmetries of a nonlinear wave equation that arises as a consequence of some Riemannian metrics of
signature −2. The objective of this study is to show how geometry can be responsible in giving rise to a nonlinear inhomogeneous
wave equation rather than assuming nonlinearities in the wave equation from physical considerations. We find Lie point symmetries
of the corresponding wave equations and give their solutions in two cases. Some interesting physical conclusions relating
to conservation laws such as energy, linear and angular momenta are also determined. 相似文献
14.
References: 《理论物理通讯》2007,47(2):333-338
For ion-acoustic waves in a plasma with non-isothermal electrons,the MKP equation is its governing equation.The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is investigated up to the third order.It indicates that the one-soliton solution of MKP equation is unstable if v = -1wheras it is stable if v = 1 until the third order approximation has been considered. 相似文献
15.
Solving Nonlinear Wave Equations by Elliptic Equation 总被引:5,自引:0,他引:5
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method. 相似文献
16.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):414-416
Abstract Group classification of the nonlinear wave equation is carried out and the conditional invariance of the wave equation with the nonlinearity F (u) = u is found. 相似文献
17.
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
18.
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
19.
20.
Mourad Bellassoued 《Communications in Mathematical Physics》2000,215(2):375-408
We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with
Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis
free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least
as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the
case of a Neumann boundary condition, even when the obstacle is a ball of ℝ3. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh
surface waves, which are connected to the failure of the Lopatinskii condition.
Received: 22 February 2000 / Accepted: 28 June 2000 相似文献