Explicit multi-symplectic method for the Zakharov–Kuznetsov equation

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

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.

Keywords: multi-symplectic method Fourier pseudospectral method Euler method Zakharov--Kuznetsov equation

Received: 30 November 2011
Revised: 05 January 2012
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Hm	(Spectral methods)

Fund: 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).

Corresponding Authors: Qian Xu
E-mail: qian429024662@sina.com

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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 2012 Chin. Phys. B 21 070206

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