A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schr
A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schr
复制标题
DOI：
10.1512/iumj.2000.49.1838
复制
发表时间：
1999-07
期刊：
影响因子：
--
通讯作者：
F. Gesztesy;Christopher K. R. T. Jones;Y. Latushkin;Milena Stanislavova
中科院分区：
文献类型：
--
作者：
F. Gesztesy;Christopher K. R. T. Jones;Y. Latushkin;Milena Stanislavova
事实证明，光谱映射定理可以解决将不变的歧管应用于非线性schr-odinger类型方程的关键问题。将理性REM应用于探测器，该操作员是在常驻波解决方案周围方程式的线性化。我们在光波导问题中出现的空间依赖性非线性的背景下提出了问题。但是，结果是更普遍地适用于更高维度甚至系统中的方程。结果是在简单且通常可验证的光谱条件下（稳定或不稳定）的常驻波（例如波导模式）的附近存在稳定，不稳定和中心的歧管。
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold the- orems to nonlinear Schr- odinger type equations. The theo- rem is applied to the operator that arises as the linearization of the equation around a standing wave solution. We cast the problem in the context of space-dependent nonlineari- ties that arise in optical waveguide problems. The result is, however, more generally applicable including to equations in higher dimensions and even systems. The consequence is that stable, unstable, and center manifolds exist in the neighborhood of a (stable or unstable) standing wave, such as a waveguide mode, under simple and commonly verifiable spectral conditions.