Average vector field methods for the coupled Schrödinger–KdV equations

doi:10.1088/1674-1056/23/7/070208

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 70208-070208.doi: 10.1088/1674-1056/23/7/070208

Average vector field methods for the coupled Schrödinger–KdV equations

张弘^a, 宋松和^{a b}, 陈绪栋^a, 周炜恩^a

a Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha 410073, China;
b State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

收稿日期:2013-11-13 修回日期:2014-01-08 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 91130013) and the Open Foundation of State Key Laboratory of High Performance Computing of China.

Average vector field methods for the coupled Schrödinger–KdV equations

Zhang Hong (张弘)^a, Song Song-He (宋松和)^{a b}, Chen Xu-Dong (陈绪栋)^a, Zhou Wei-En (周炜恩)^a

a Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha 410073, China;
b State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received:2013-11-13 Revised:2014-01-08 Online:2014-07-15 Published:2014-07-15
Contact: Song Song-He E-mail:shsong@nudt.edu.cn
About author:02.60.Cb; 02.70.Bf; 02.30.Jr
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 91130013) and the Open Foundation of State Key Laboratory of High Performance Computing of China.

摘要/Abstract

摘要： The energy preserving average vector field (AVF) method is applied to the coupled Schrödinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.

关键词: coupled Schrö, dinger-KdV equations, average vector field method, splitting method, Fourier pseudospectral method

Abstract: The energy preserving average vector field (AVF) method is applied to the coupled Schrödinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.

Key words: coupled Schrö, dinger-KdV equations, average vector field method, splitting method, Fourier pseudospectral method

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.70.Bf (Finite-difference methods) 02.30.Jr (Partial differential equations)

张弘, 宋松和, 陈绪栋, 周炜恩. Average vector field methods for the coupled Schrödinger–KdV equations[J]. 中国物理B, 2014, 23(7): 70208-070208.

Zhang Hong (张弘), Song Song-He (宋松和), Chen Xu-Dong (陈绪栋), Zhou Wei-En (周炜恩). Average vector field methods for the coupled Schrödinger–KdV equations[J]. Chin. Phys. B, 2014, 23(7): 70208-070208.

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Average vector field methods for the coupled Schrödinger–KdV equations

Average vector field methods for the coupled Schrödinger–KdV equations

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