Commun. Comput. Phys., 16 (2014), pp. 35-55.

Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation

Yuezheng Gong 1, Jiaxiang Cai 1, Yushun Wang 1*

1 Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. China.

Received 9 March 2013; Accepted (in revised version) 4 November 2013
Available online 28 March 2014


In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effectiveness of the proposed methods will be demonstrated by a number of numerical examples. The numerical results also confirm that the global energy and momentum are well preserved.

AMS subject classifications: 65M06, 65M70, 65T50, 65Z05, 70H15

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Key words: Kawahara equation, Multi-symplecticity, Fourier pseudospectral method, FFT.

*Corresponding author.
Email: (Y. Wang), (Y. Gong), (J. Cai)

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