Multi-symplectic method for the coupled Schrödinger-KdV equations

doi:10.1088/1674-1056/23/8/080204

›› 2014, Vol. 23 ›› Issue (8): 80204-080204.doi: 10.1088/1674-1056/23/8/080204

Multi-symplectic method for the coupled Schrödinger-KdV equations

张弘^a, 宋松和^{a b}, 周炜恩^a, 陈绪栋^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:2013-11-01 修回日期:2014-02-11 出版日期:2014-08-15 发布日期:2014-08-15
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.

Multi-symplectic method for the coupled Schrödinger-KdV equations

Zhang Hong (张弘)^a, Song Song-He (宋松和)^{a b}, Zhou Wei-En (周炜恩)^a, Chen Xu-Dong (陈绪栋)^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:2013-11-01 Revised:2014-02-11 Online:2014-08-15 Published:2014-08-15
Contact: Song Song-He E-mail:shsong@nudt.edu.cn
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.

摘要/Abstract

摘要： In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson (CN) method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.

关键词: coupled Schrö, dinger-KdV equations, multi-symplectic, Fourier pseudospectral method

Abstract: In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson (CN) method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.

Key words: coupled Schrödinger-KdV equations, multi-symplectic, 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, 周炜恩, 陈绪栋. Multi-symplectic method for the coupled Schrödinger-KdV equations[J]. , 2014, 23(8): 80204-080204.

Zhang Hong (张弘), Song Song-He (宋松和), Zhou Wei-En (周炜恩), Chen Xu-Dong (陈绪栋). Multi-symplectic method for the coupled Schrödinger-KdV equations[J]. Chin. Phys. B, 2014, 23(8): 80204-080204.

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Multi-symplectic method for the coupled Schrödinger-KdV equations

Multi-symplectic method for the coupled Schrödinger-KdV equations

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