Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

doi:10.1088/1674-1056/21/7/070206

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70206-070206.doi: 10.1088/1674-1056/21/7/070206

Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

钱旭, 宋松和, 高二, 李伟斌

Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China

收稿日期:2011-11-30 修回日期:2012-01-05 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10971226, 91130013, and 11001270) and the National Basic Research Program of China (Grant No. 2009CB723802).

Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

Qian Xu(钱旭)^†, Song Song-He(宋松和), Gao Er(高二), and Li Wei-Bin(李伟斌)

Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China

Received:2011-11-30 Revised:2012-01-05 Online:2012-06-01 Published:2012-06-01
Contact: Qian Xu E-mail:qian429024662@sina.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10971226, 91130013, and 11001270) and the National Basic Research Program of China (Grant No. 2009CB723802).

摘要/Abstract

摘要： We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov--Kuznetsov equation. The method is is to combine the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.

关键词: multi-symplectic method, Fourier pseudospectral method, Euler method, Zakharov--Kuznetsov equation

Abstract: We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov--Kuznetsov equation. The method is is to combine the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.

Key words: multi-symplectic method, Fourier pseudospectral method, Euler method, Zakharov--Kuznetsov equation

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations) 02.70.Hm (Spectral methods)

钱旭, 宋松和, 高二, 李伟斌. Explicit multi-symplectic method for the Zakharov–Kuznetsov equation[J]. 中国物理B, 2012, 21(7): 70206-070206.

Qian Xu(钱旭), Song Song-He(宋松和), Gao Er(高二), and Li Wei-Bin(李伟斌) . Explicit multi-symplectic method for the Zakharov–Kuznetsov equation[J]. Chin. Phys. B, 2012, 21(7): 70206-070206.

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Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

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