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An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation

Published online by Cambridge University Press:  28 May 2015

Hanquan Wang  and
Lina Yanti
Hanquan Wang*
Affiliation:
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan Province, 650221, P. R. China. Department of Mathematics, National University of Singapore, 117543, Singapore
Lina Yanti*
Affiliation:
Department of Mathematics, National University of Singapore, 117543, Singapore
*
Corresponding author.Email address:hanquan.wang@gmail.com
Corresponding author.Email address:linayanti@nus.edu.sg
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Abstract

In this paper, we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation. Using the Strang time-splitting technique, we split the equation into linear part and nonlinear part. The linear part is solved with Fourier Pseudospectral method; the nonlinear part is solved analytically. We show that the method is easy to be applied and second-order in time and spectrally accurate in space. We apply the method to investigate soliton propagation, soliton interaction, and generation of stable moving pulses in one dimension and stable vortex solitons in two dimensions.

Keywords

65M7065Z05Quintic complex Swift-Hohenberg equationtime-splitting Fourier pseudospectral methodnumerical simulationsoliton
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 2 , May 2011 , pp. 237 - 254
Copyright
Copyright © Global Science Press Limited 2011

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