An extension of the stability index for traveling-wave solutions and its application to bifurcations
An extension of the stability index for traveling-wave solutions and its application to bifurcations
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行波解稳定性指标的推广及其在分岔问题中的应用
DOI：
10.1137/s003614109427878x
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发表时间：
1997
影响因子：
2
通讯作者：
Shunsaku Nii
中科院分区：
文献类型：
--
作者：
Shunsaku Nii
本文讨论了一维反应扩散方程行波解的稳定性指数[J]。Reine Angew。数学。， 410 (1990), pp. 167—212]。给出了稳定性指标的一个扩展，使该指标对摄动具有鲁棒性，并利用该扩展证明了行波粘接分岔的一个加性公式。我们还考虑了某些异斜分岔的应用，并讨论了其中的一些具体例子。
We treat the stability index for traveling-wave solutions of one-dimensional reaction-diffusion equations due to Alexander, Gardner, and Jones [J. Reine Angew. Math., 410 (1990), pp. 167--212]. An extension of the stability index which makes the index robust to perturbation is given and, using the extension, an additive formula for a gluing bifurcation of traveling waves is proven. Wealso consider certain heteroclinic bifurcations as an application, some specific examples of which are discussed.