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1.
Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients 下载免费PDF全文
In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. 相似文献
2.
Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity 下载免费PDF全文
Local structure-preserving algorithms including multi-symplectic, local energy-and momentum-preserving schemes are proposed for the generalized Rosenau–RLW–Kd V equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time–space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants. 相似文献
4.
非线性Pochhammer-Chree方程的多辛格式 总被引:4,自引:0,他引:4
提出非线性Pochhammer—Chree方程的多辛形式,进而得到一个等价于中心Preissmann积分的15点多辛格式.数值例子表明:多辛格式具有良好的长时间数值行为。 相似文献
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Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性. 相似文献
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Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multi-symplectic splitting(MSS) method to solve the two-dimensional nonlinear Schrödinger equation (2D-NLSE) in this paper. It is further shown that the method constructed in this way preserve the global symplecticity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness
of the proposed method. 相似文献
8.
Weipeng HU Zhen WANG Yulu HUAI Xiqiao FENG Wenqi SONG Zichen DENG 《应用数学和力学(英文版)》2022,43(10):1503-1514
Applied Mathematics and Mechanics - Solvent-free nanofluids hold promise for many technologically significant applications. The liquid-like behavior, a typical rheological property of solvent-free... 相似文献
9.
In this paper,the complex multi-symplectic method and the implementation of the generalized sinhGordon equation are investigated in detail.The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly.The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws(including a multi-symplectic conservation law(CLS),a local energy conservation law(ECL) as well as a local momentum conservation law(MCL)) is constr... 相似文献
10.
THE MULTI-SYMPLECTIC ALGORITHM FOR “GOOD” BOUSSINESQ EQUATION 总被引:2,自引:0,他引:2
The multi-symplectic formulations of the “Good” Boussinesq equation were considered. For the multi-symplectic formulation,
a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical
experiments show that the multi-symplectic scheme have excellent long-time numerical behavior.
Foundation items: the Foundation for Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering
Computing, Chinese Academy of Sciences; the Natural Science Foundation of Huaqiao University.
Biography: ZENG Wen-ping (1940-), Professor (E-mail: qmz@1sec.cc.ac.cn) 相似文献