We present a numerical approach for determination of the spectral stability of solitary waves by computing eigenvalues and eigenfunctions of the corresponding eigenvalue problems, along with their continuation, for nonlinear wave equations in one space dimension. We illustrate the approach for the nonlinear Schrodinger (NLS) equation with a small potential, and numerically determine the spectral stability of solitary waves near bifurcation points along with computations of eigenfunctions and eigenvalues. The numerical results demonstrate some theoretical ones the authors recently obtained for the example.

中文翻译：

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分岔点附近孤立波谱稳定性的数值分析

我们提出了一种通过计算对应特征值问题的特征值和特征函数以及它们的延拓来确定孤立波谱稳定性的数值方法，用于一个空间维度中的非线性波动方程。我们说明了具有小电位的非线性薛定谔（NLS）方程的方法，并数值确定了分岔点附近孤立波的光谱稳定性以及特征函数和特征值的计算。数值结果证明了作者最近为该示例获得的一些理论结果。