A New Approach to Sideband-Instabilities Using the Principle of Reduced Instability
A New Approach to Sideband-Instabilities Using the Principle of Reduced Instability
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利用减少不稳定性原理解决边带不稳定性的新方法
DOI：
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发表时间：
1995
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通讯作者：
A. Mielke
中科院分区：
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作者：
A. Mielke
首先，我们发展了约化不稳定性理论，通过Liapunov{施密特约化来分析分支解的稳定性。其次，这一理论被推广到覆盖边带不稳定性，使用Floquet分析。该方法适用于辊图案的Swift{Hohenberg方程作为模式的图案形成。我们分析了小轧辊的稳定性问题分析计算的边带向量的临界特征值的扩展。因此，我们恢复了埃克豪斯和曲折的不稳定性。最后，我们将计算结果与纽韦尔{Whitehead}方程的预测结果进行了比较，得到了很好的一致性.
First we develop the theory of reduced instability in order to analyze stability of bifurcating solutions via the Liapunov{Schmidt reduction. Next, this theory is generalized to cover sideband instabilities using a Floquet ansatz. The method is applied to roll patterns in the Swift{Hohenberg equation which serves as a model for pattern formation. We analyze the stability problem of small rolls analytically by calculating expansions of the critical eigenvalues in terms of the sideband vector. Thus we recover the Eckhaus and the zigzag instability. Finally, we compare the results with the predictions of the Newell{Whitehead equation and obtain good agreement.