一维三次非线性散焦 Schrödinger 方程 Lax 算子的特征值分析
偏微分方程分析
2023-02-02 v2
摘要
我们刻画了与一维三次非线性散焦 Schr"odinger 方程相关的 Lax 算子的特征值位置与数量。借助一个新发现的酉矩阵，该分析化简为对一个酉等价算子的谱问题研究，该算子仅涉及势的振幅与相速度。我们研究了具有特殊振幅与相速度的势的实例。
引用
@article{arxiv.2207.05186,
title = {Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schr\"odinger equation},
author = {Xian Liao and Michael Plum},
journal= {arXiv preprint arXiv:2207.05186},
year = {2023}
}
备注
The number of eigenvalues for more general cases is characterized. Some interesting examples of potentials with piecewise-constant amplitude and phase velocity functions are included