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In this paper,we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger(DNLS) equation.Based on its damped multi-symplectic formulation,the DNLS system can be split into a Hamiltonian part and a dissipative part.For the Hamiltonian part,the average vector field(AVF) method and implicit midpoint method are employed in spatial and temporal discretizations,respectively.For the dissipative part,we can solve it exactly.The proposed method conserves the conformal momentum conservation law in any local time-space region.With periodic boundary conditions,this method also preserves the total conformal momentum and the dissipation rate of momentum exactly.Numerical experiments are presented to demonstrate the conservative properties of the proposed method. 相似文献
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The calculation of elastic deformations of corrugated diaphragms was given by orthogonal anisotropy plate theory[1], and its result agrees with the experimental results. But it has never been discussed seriously how the number and form of convolutions affect the elastic deformations and stress distributions of anisotropy plate. As a result, adaptable limits of orthogonal anisotropy plate theory cannot be indicated when it is used to calculate diaphragms. It is said that the theory is fairly good for calculating elastic deformations of the diaphragms which have more convolutions. It is also said that the error in calculating stresses is rather large. This paper, by using the toroidal shell theory, presents the calculation of deformations and stresses of three-convolution circular arc corrugated diaphragms both symmetrical and unsymmetrical, compares its result with that of the orthogonal anisotropy plate theory and gives definite adaptable limits of the latter theory. 相似文献
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We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation. 相似文献
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** Email: kzhang{at}math.cuhk.edu.hk The non-linear wave equation is taken as a model problem forthe investigation. Different multi-symplectic reformulationsof the equation are discussed. Multi-symplectic RungeKuttamethods and multi-symplectic partitioned RungeKutta methodsare explored based on these different reformulations. Some popularand efficient multi-symplectic schemes are collected and constructed.Stability analyses are performed for these schemes. 相似文献
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This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect. 相似文献