[1]徐远,孔令华,王兰,等.带有阻尼项的4阶非线性薛定谔方程的显式辛格式[J].江西师范大学学报(自然科学版),2013,(03):244-248.
 XU Yuan,KONG Ling-hua,WANG Lan,et al.Explicit Symplectic Scheme for Nonlinear Fourth Order Schr(o)dinger Equation with a Trapped Term[J].,2013,(03):244-248.
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带有阻尼项的4阶非线性薛定谔方程的显式辛格式()
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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03期
页码:
244-248
栏目:
出版日期:
2013-05-01

文章信息/Info

Title:
Explicit Symplectic Scheme for Nonlinear Fourth Order Schr(o)dinger Equation with a Trapped Term
作者:
徐远;孔令华;王兰;黄晓梅
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
XU Yuan;KONG Ling-hua;WANG Lan;HUANG Xiao-mei
关键词:
4阶非线性薛定谔方程显式辛格式哈密尔顿系统
Keywords:
fourth-order Schr(o)dinger equationexplicit symplectic schemeHamiltonian system
分类号:
O241.8
文献标志码:
A
摘要:
把带有阻尼项的4阶薛定谔方程写成标准的哈密尔顿系统,将该哈密尔顿系统分裂成2个哈密尔顿子系统.一个子系统是可分的,可以构造显式的辛格式;而另一个子系统由点点的质量守恒可以精确求解.这样得到的数值格式整体上是辛格式,而且避免了通常辛格式需要迭代的弊端,提高了计算效率.
Abstract:
The Schrödinger equation with trapped term is rewrited into standard Hamiltonian system,which is splitted into two subsystems.One of them is separable and explicit symplectic scheme can be constructed.Another can be solved exactly due to its pointwise mass conservation law.The whole scheme is explicit symplectic integrator.Therefore,no iterative is required and computational efficiency is improved.

参考文献/References:

[1] 冯康,秦孟兆.哈密尔顿系统的辛几何算法 [M].杭州:浙江科学技术出版社,2002.
[2] Zeng Wenping.A leap frog finite difference scheme for a class of nonlinear Schrödinger equations of high order [J].J Comput Math,1999,17(2):133-138.
[3] Kong Linghua,Hong Jialin,Wang Lan,et al.Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term [J].J Comput Appl Math,2009,231(2):664-679.
[4] Hong Jialin,Jiang Shanshan,Li Chun.Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations [J].J Comput Phys,2009,228(9):3517-3532.
[5] Kong Linghua,Cao Ying,Wang Lan,et al.Split-step multisymplectic integrator for the fourth-order Schrödinger equation with cubic nonlinear term [J].J Chin Comput Phys,2011,28(5):76-82.
[6] 黄红,王兰.薛定谔方程的局部1维多辛算法 [J].江西师范大学学报:自然科学版,2011,35(5):455-458.
[7] 王兰.多辛Preissmann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.
[8] 王兰,陈静.2维Schrödinger方程的多辛格式 [J].江西师范大学学报:自然科学版,2010,34(6):600-604.
[9] Miller J H.On the location of zeros of certain class of polynomials with application to numerical analysis [J].J Inst Math Appl,1971,8(3):397-406.
[10] Qin Mengzhao,Zhang Meiqing.Mutil-stage symplectic schemes of two kinds of Hamiltonian systems for wave equations [J].Computer Math Appl,1990,19(10):51-62.
[11] 符芳芳,孔令华,王兰.一类新的含双幂非线性项的Schrödinger方程的差分格式 [J].江西师范大学学报:自然科学版,2010,34(1):22-26.

备注/Memo

备注/Memo:
国家自然科学基金(10901074,11271171);江西省自然科学基金(20114BAB201011);江西省教育厅科研计划(GJJ12174)
更新日期/Last Update: 1900-01-01