论文标题
$ \ mathbb {r} $上线性哈密顿系统的Maslov索引和光谱计数
The Maslov index and spectral counts for linear Hamiltonian systems on $\mathbb{R}$
论文作者
论文摘要
使用$ \ mathbb {r} $上指定的一般线性哈密顿系统系统，我们开发了一个框架，将Maslov索引与该系统在表单$ [λ_1，λ_2）$和$（ - \ fiffty，λ_2）$的间隔内具有的特征值数量联系起来。我们验证我们的框架是否可以针对Sturm-Liouville系统，四阶潜在系统以及光谱参数中的非线性系统实施。该分析主要是由应用于非线性波的光谱稳定性的应用，并强调了此类分析的各个方面。
Working with a general class of linear Hamiltonian systems specified on $\mathbb{R}$, we develop a framework for relating the Maslov index to the number of eigenvalues the systems have on intervals of the form $[λ_1, λ_2)$ and $(-\infty, λ_2)$. We verify that our framework can be implemented for Sturm-Liouville systems, fourth-order potential systems, and a family of systems nonlinear in the spectral parameter. The analysis is primarily motivated by applications to the analysis of spectral stability for nonlinear waves, and aspects of such analyses are emphasized.
