Average vector field methods for the coupled Schrödinger–KdV equations

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

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.

Keywords: coupled Schrö dinger-KdV equations average vector field method splitting method Fourier pseudospectral method

Received: 13 November 2013
Revised: 08 January 2014
Accepted manuscript online:

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Bf	(Finite-difference methods)
	02.30.Jr	(Partial differential equations)

Fund: 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.

Corresponding Authors: Song Song-He
E-mail: shsong@nudt.edu.cn

About author: 02.60.Cb; 02.70.Bf; 02.30.Jr

Cite this article:

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 2014 Chin. Phys. B 23 070208

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