An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation
Hanquan Wang 1*, Lina Yanti 21 School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan Province, 650221, P. R. China; and Department of Mathematics, National University of Singapore, 117543, Singapore.
2 Department of Mathematics, National University of Singapore, 117543, Singapore.
Received 21 June 2010; Accepted (in revised version) 16 November 2010
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.AMS subject classifications: 65M70, 65Z05
Key words: Quintic complex Swift-Hohenberg equation, time-splitting Fourier pseudospectral method, numerical simulation, soliton.
Email: firstname.lastname@example.org (H. Wang), email@example.com (L. Yanti)