论文标题
非线性特征值方法的非线性波的线性稳定性
Nonlinear eigenvalue methods for linear pointwise stability of nonlinear waves
论文作者
论文摘要
我们提出了一种迭代方法，可以在基本上是一维域上构成的线性问题中找到偶有的增长指数增长率。这种刻度的生长速率捕获了扩展系统中的稳定性和不稳定性，并作为矩阵家族的光谱值出现，这些矩阵家族在分析上取决于光谱参数，这是通过散射类型问题获得的。与依赖于该非线性矩阵铅笔计算决定因素的文献方法不同，我们提出和分析了一种逆权力方法，该方法允许人们稳健地定位与复杂平面中给定参考点的最接近的光谱值。该方法在没有先验知识的情况下找到了分支点，特征值和共振杆。
We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems and arise as spectral values of a family of matrices that depends analytically on a spectral parameter, obtained via a scattering-type problem. Different from methods in the literature that rely on computing determinants of this nonlinear matrix pencil, we propose and analyze an inverse power method that allows one to locate robustly the closest spectral value to a given reference point in the complex plane. The method finds branch points, eigenvalues, and resonance poles without a priori knowledge.
