论文标题
反应扩散系统中的索引理论与偏斜梯度结构
Index theory for traveling waves in reaction diffusion systems with skew gradient structure
论文作者
论文摘要
在先前的论文[9]中已经建立了一种统一的几何方法，用于对具有偏斜梯度结构的反应扩散方程的稳定性分析[9]，但基本上在旅行前溶液的情况下没有发现结果。在这项工作中，我们将弥合这一差距。在这种情况下，波动波的Maslov指数定义明确，我们将展示如何使用它来提供波浪的光谱信息。作为一个应用程序，我们使用相同的索引，提供了Fitzhugh-Nagumo方程的旅行前解决方案的确切数量。
A unified geometric approach for the stability analysis of traveling pulse solutions for reaction-diffusion equations with skew-gradient structure has been established in a previous paper [9], but essentially no results have been found in the case of traveling front solutions. In this work, we will bridge this gap. For such cases, a Maslov index of the traveling wave is well-defined, and we will show how it can be used to provide the spectral information of the waves. As an application, we use the same index providing the exact number of unstable eigenvalues of the traveling front solutions of FitzHugh-Nagumo equation.
