带三次非线性项的四阶Schrödinger方程的分裂多辛算法

计算物理 ›› 2011, Vol. 28 ›› Issue (5): 730-736.

带三次非线性项的四阶Schrödinger方程的分裂多辛算法

孔令华¹, 曹莹¹, 王兰¹, 万隆²

1. 江西师范大学数学与信息科学学院, 江西南昌 330022;
2. 南昌师范高等专科学校自然科学系, 江西南昌 330029

收稿日期:2010-11-09 修回日期:2011-04-22 出版日期:2011-09-25 发布日期:2011-09-25
作者简介:孔令华(1977-),male,Shi cheng Jiang xi,associate professor,Major in numerical methods for PDEs,E-mail:konglh@mail.ustc.edu.cn
基金资助:
National Natural Science Foundation of China(10901074);Provincial Natural Science Foundation of Jiangxi(2008GQS0054);Postgraduate Innovation Foundation of Jiangxi Normal University(YJS2010009)

Split-step Multisymplectic Integrator for Fourth-order Schrödinger Equation with Cubic Nonlinear Term

KONG Linghua¹, CAO Ying¹, WANG Lan¹, WAN Long²

1. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
2. Department of Natural Science, Nanchang Teachers College, Nanchang 330029, China

Received:2010-11-09 Revised:2011-04-22 Online:2011-09-25 Published:2011-09-25
Supported by:
National Natural Science Foundation of China(10901074);Provincial Natural Science Foundation of Jiangxi(2008GQS0054);Postgraduate Innovation Foundation of Jiangxi Normal University(YJS2010009)

摘要/Abstract

摘要： 对-类带三次非线性项的四阶SchrÖdinger方程提出分裂多辛格式。其基本思想是将多辛算法和分裂方法相结合,既具有多辛格式固有的保多辛几何结构的特性,又发挥了分裂方法在计算上灵活高效的特点。数值实验结果表明,分裂多辛格式比其它传统的多辛格式更节约计算时间和计算机的内存,从而更加优越.

关键词: 四阶NSL方程, 多辛格式, 分裂方法

Abstract: A split--step muhisympleetic scheme is proposed for a kind of fourth-order Schrödinger equations with eubie nonlinear term.Ihe basic idea is to combine muhisymplectic integrator with split-step method.The method not only preserves muhisymplectic structure of multisympleetie integrators,but also has the virtue of efficiency and flexibility of split-step method in computation.Numerical experiments show that the split-step muhisympleetic method is more economic in computational time and computer memory than traditional muhisymplectic integrator.

Key words: fourth-order NSL equation, muhisymplectic scheme, split-step method

中图分类号:

O241.82

孔令华, 曹莹, 王兰, 万隆. 带三次非线性项的四阶Schrödinger方程的分裂多辛算法[J]. 计算物理, 2011, 28(5): 730-736.

KONG Linghua, CAO Ying, WANG Lan, WAN Long. Split-step Multisymplectic Integrator for Fourth-order Schrödinger Equation with Cubic Nonlinear Term[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(5): 730-736.

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