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Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation

Published online by Cambridge University Press:  03 June 2015

Yuezheng Gong ,
Jiaxiang Cai  and
Yushun Wang
Yuezheng Gong*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. China
Jiaxiang Cai*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. China
Yushun Wang*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. China
*
Email:gyz8814@aliyun.com
Email:thomasjeer@sohu.com
Corresponding author.Email:wangyushun@njnu.edu.cn
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Abstract

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.

Keywords

65M0665M7065T5065Z0570H15Kawahara equationMulti-symplecticityFourier pseudospectral methodFFT.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 1 , July 2014 , pp. 35 - 55
Copyright
Copyright © Global Science Press Limited 2014

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