Bifurcation Analysis of the 1D and 2D Generalized swift-Hohenberg equation
Bifurcation Analysis of the 1D and 2D Generalized swift-Hohenberg equation
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DOI：
10.1142/s0218127410025922
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发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
Hongjun Gao;Qingkun Xiao
中科院分区：
文献类型：
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作者：
Hongjun Gao;Qingkun Xiao
本文研究了广义Swift-Hohenberg方程的分支问题。我们首先研究了一维广义Swift-Hohenberg方程在三种边界条件下的分支。利用Liapunov-Schmidt约化方法，将原方程转化为约化系统，并进行了分叉分析。其次，研究了二维广义Swift-Hohenberg方程在周期边界条件下的分支问题，利用摄动方法得到了平凡解分支的非平凡解的渐近表达式。此外，还讨论了分支解的稳定性。
In this paper, bifurcation of the generalized Swift–Hohenberg equation is considered. We first study the bifurcation of the generalized Swift–Hohenberg equation in one spatial dimension with three kinds of boundary conditions. With the help of Liapunov–Schmidt reduction, the original equation is transformed to the reduced system, and then the bifurcation analysis is carried out. Secondly, bifurcation of the generalized Swift–Hohenberg equation in two spatial dimensions with periodic boundary conditions is also considered, using the perturbation method, asymptotic expressions of the nontrivial solutions bifurcated from the trivial solution are obtained. Moreover, the stability of the bifurcated solutions is discussed.