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Volume 4, Issue 2
An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation

Hanquan Wang & Lina Yanti

DOI: 10.4208/nmtma.2011.42s.7

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 237-254.

Published online: 2011-04

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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

Quintic complex Swift-Hohenberg equation, time-splitting Fourier pseudospectral method, numerical simulation, soliton.

  • AMS Subject Headings

65M70, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{NMTMA-4-237, author = {Hanquan Wang and Lina Yanti}, title = {An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {2}, pages = {237--254}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.42s.7}, url = {http://global-sci.org/intro/article_detail/nmtma/5967.html} }
TY - JOUR T1 - An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation AU - Hanquan Wang & Lina Yanti JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 237 EP - 254 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.42s.7 UR - https://global-sci.org/intro/article_detail/nmtma/5967.html KW - Quintic complex Swift-Hohenberg equation, time-splitting Fourier pseudospectral method, numerical simulation, soliton. AB -

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.

Hanquan Wang and Lina Yanti. (2011). An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation. Numerical Mathematics: Theory, Methods and Applications. 4 (2). 237-254. doi:10.4208/nmtma.2011.42s.7
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