[1]黄浪扬.“Good”Boussinesq方程的多辛Fourier拟谱算法[J].华侨大学学报(自然科学版),2007,28(1):92-95.[doi:10.3969/j.issn.1000-5013.2007.01.024]
　HUANG Lang-yang.Multisymplectic Fourier Pseudo-Spectral Algorithm for "Good" Boussinesq Equation[J].Journal of Huaqiao University(Natural Science),2007,28(1):92-95.[doi:10.3969/j.issn.1000-5013.2007.01.024]
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“Good”Boussinesq方程的多辛Fourier拟谱算法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第28卷
期数:
2007年第1期
页码:
92-95
栏目:
出版日期:
2007-01-20

文章信息/Info

Title:
Multisymplectic Fourier Pseudo-Spectral Algorithm for "Good" Boussinesq Equation
文章编号:
1000-5013(2007)01-0092-04
作者:
黄浪扬
华侨大学数学系 福建泉州362021
Author(s):
HUANG Lang-yang
Department of Mathematics, Huaqiao University, Quanzhou 362021, China
关键词:
多辛方程组;  Fourier拟谱格式;  非线性“good”Boussinesq方程;  数值实验
Keywords:
multisymplectic systems;  Fourier pseudo-spectral scheme;  nonlinear "Good" Boussinesq equation;  numerical experiment
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2007.01.024
文献标志码:
A
摘要:
对满足周期边界条件的非线性“good”Boussinesq方程作正则变换,得到它的一个多辛方程组及其守恒律.在空间方向用Fourier拟谱方法离散此方程组,然后在时间方向用中点辛格式对半离散方程进行数值求解,得到了非线性“good”Boussinesq方程的多辛Fourier拟谱格式,同时也得到格式的半离散及全离散多辛守恒律.数值实验能很好地模拟原孤立波的运动,验证了所构造格式的有效性与长时间的数值稳定性.
Abstract:
By canonical transformation,multisymplectic systems and multisymplectic conservation laws for nonlinear "Good" Boussinesq equation with periodic boundary conditions are obtained.Using Fourier pseudo-spectral method in spatial direction and mid-point Euler method in time direction to the multisymplectic systems,a multisymplectic Fourier pseudo-spectral scheme is constructed.At the same time,we have also obtained semi-discrete and full-discrete multisymplectic conservation laws for the scheme.Numerical experiments show that the multisymplectic Fourier pseudo-spectral scheme constructed in this paper is effective,and has excellent long-time numerical behavior.

参考文献/References:

[1] BRIDGES T J, REICH S. Multi-symplectic integrators:Numerical schemes for Hamiltonian PDEs that conserve symplecticity [J]. Physics Letters A, 2001, (4-5):184-193.doi:10.1016/S0375-9601(01)00294-8.
[2] BRIDGES T J. Multi-symplectic structures and wave propagation [J]. Math Proc Cam Phil Soc, 1997.147-190.doi:10.1017/S0305004196001429.
[3] REICH S. Multi-symplectic Runge-Kutta methods for Hamiltonian wave equations [J]. Journal of Computational Physics, 2000(5):473-499.
[4] BRIDGES T J, REICH S. Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations [J]. Physica D, 2001():491-504.doi:10.1016/S0167-2789(01)00188-9.
[5] CHEN Jing-bo, QIN Meng-zhao. Multi-symplectic Fourier pseudospectral method for the nonlinear Schrdinger equation [J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2001.193-204.
[6] ISLAS A L, SCHOBER C M. Multi-symplectic spectral methods for the Gross-Pitaevski equation [J]. Lecture Notes In Computer Science, 2002.486-495.doi:10.1007/3-540-47789-6_51.
[7] 曾文平, 黄浪扬, 秦孟兆. "Good" Boussinesq 方程的多辛算法 [J]. 应用数学和力学, 2002(7):743-748.doi:10.3321/j.issn:1000-0887.2002.07.012.

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备注/Memo

备注/Memo:
福建省自然科学基金计划资助项目(Z0511029)
更新日期/Last Update: 2014-03-23