[1]王兰,符芳芳,童慧.Dirac方程分裂步多辛格式[J].江西师范大学学报(自然科学版),2013,(05):462-465.
　WANG Lan,FU Fang-fang,TONG Hui.The Split-Step Multisymplectic Scheme for Dirac Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(05):462-465.
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Dirac方程分裂步多辛格式()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2013年05期
页码:
462-465
栏目:
出版日期:
2013-10-31

文章信息/Info

Title:
The Split-Step Multisymplectic Scheme for Dirac Equation
作者:
王兰;符芳芳;童慧
江西师范大学数学与信息科学学院,江西南昌,330022；南昌工学院基础部,江西南昌,330108
Author(s):
WANG Lan；FU Fang-fang；TONG Hui
关键词:
Dirac方程; 分裂步方法; 多辛格式; 计算效率
Keywords:
Dirac equation; split-step method; symplectic scheme; computational efficiency
分类号:
O241.8
文献标志码:
A
摘要:
把非线性的Dirac方程分裂成线性和非线性2个子问题,这2个子问题具有辛或者多辛结构,可以用辛格式对它们进行离散计算,得到的格式具有整体辛性.此格式较传统的多辛格式具有效率高、计算快等优点.
Abstract:
One splits the Dirac equation into a linear subproblem and a nonlinear subproblem.The subproblems are equipped with symplectic or multisymplectic structures.Then,they are approximated by symplectic integrators.As a whole,the scheme is symplectic.It is superior to the traditional multisymplectic integrator in efficiency and computational cost.

参考文献/References:

[1] Alvarez A,Carreras B.Interaction dynamics for the solitary waves of a nonlinear Dirac model [J].Phys Lett A,1981,86(6/7):327-332.
[2] Alvarez A.Linear Crank-Nicholson scheme for nonlinear Dirac equations [J].J Comput Phys,1992,99(2):348-350.
[3] Alvarez A,Kuo Penyu,Vazquez L.The numerical study of a nonlinear one-dimensional Dirac equation [J].Appl Math Comput,1983,13(1/2):1-15.
[4] Hong Jialin,Li Chun.Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations [J].J Comput Phys,2006,211(2):448-472.
[5] Wang Han,Tang Huazhong.An efficient adaptive mesh redistribution method for a nonlinear Dirac equation [J].J Comput Phys,2007,222:176-193.
[6] Wang Yushun,Hong Jialin.Multi-symplectic algorithms for Hamiltonian partial differential equations [J].Commun Appl Math Comput 2013,27:163-230.
[7] Hong Jialin,Kong Linghua.Novel multisymplectic integrators for nonlinear fourth-order Schrödinger equation with trapped term [J].Commun Comput Phys,2010,7(3):613-630.
[8] Kong Linghua,Cao Ying,Wang Lan,et al.Split-step multisymplectic integrator for the fourth-order Schrödinger equation with cubic nonlinear term [J].Chin J Comput Phys,2011,28(5):730-736.
[9] 王兰.多辛Preissman格式及其应用 [J].江西师范大学学报:自然科学版,2009,33(1):42- 46.
[10] 黄红,王兰.薛定谔方程的局部1维多辛格式 [J].江西师范大学学报:自然科学版,2011,35(5):455-458.
[11] 郑斌.2+1维非线性Schrödinger方程的显式解 [J].重庆师范大学学报:自然科学版,2006,23(2):23-25.

备注/Memo

备注/Memo:
国家自然科学基金(11211171,11301234)；江西省自然科学基金(20114BAB201011)；江西省教育厅基金(GJJ12174)
更新日期/Last Update: 1900-01-01