Spatiotemporal complexity of the cubic Ginzburg-Landau equation |
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| Authors: | Boling Guo Zhujung Jing Bainian Lu |
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| Affiliation: | aCenter for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;aInstitute of Mathematics, Academia Sinica, Beijing 100080, China;bDepartment of Mathematics, Shaanxi Normal University, Xi'an, 710062 Shaanxi, China;cLaboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | The linear dispersive relation of the travelling-wave solution is investigated for cubic G-L equation. Moreover, the relation among the parameter c0, the amplitude |μo| and the most unstable wave number q is discussed. Then convergence of an unconditionally stable, explicit pseudo-spectral scheme is proved by energy estimates. Finally, by using the proposed scheme, the chaotic attractor, bifurcation structure and asymptotic dynamics are obtained. The results show there exist two different types of chaotic attractors for the most unstable wave number qo and was fixed the amplitude |μo| in the same one system. |
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| Keywords: | Ginzburg-Landau equation Pesudo-spectral Methods Bifurcation Chaos |
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