Data analysis and reduction using stationary solutions of the NLS equation
Data analysis and reduction using stationary solutions of the NLS equation
复制标题
使用 NLS 方程的平稳解进行数据分析和简化
DOI：
10.1080/00036810903569481
复制
发表时间：
2010
影响因子：
1.1
通讯作者：
David O. Lovit
中科院分区：
文献类型：
--
作者：
B. Deconinck;David O. Lovit
我们证明了非线性薛定谔方程（NLS）的定态解产生了具有周期边界条件的平方可积函数的标准正交基族。这允许我们以与常规傅立叶模式或其他基组相同的方式使用这些解。例如，我们展示了NLS基组用于数据分析的适用性，以及作为获得简化模型的一种手段。使用各种各样的例子，我们表明，与NLS基组的工作是有利的傅立叶模式，它们包含作为一个特殊的情况下的工作。NLS集是特别有吸引力的NLS方程预计提供一个很好的描述任何潜在的动态，如在深水或非线性光学调制波的描述的问题。在这些情况下，与常规傅立叶分析相比，实验数据的分解需要更少的模式，并且截断的分量在更长的时间尺度上仍然不重要。
We demonstrate that the stationary solutions of the nonlinear Schrödinger equation (NLS) give rise to families of orthonormal bases for the square integrable functions with periodic boundary conditions. This allows us to use these solutions in the same way as regular Fourier modes or other basis sets. For instance, we show the applicability of the NLS basis sets for doing data analysis, and as a means for obtaining reduced models. Using a variety of examples, we show that working with the NLS basis sets is advantageous over working with the set of Fourier modes, which they contain as a special case. The NLS sets are particularly appealing for those problems where the NLS equation is expected to provide a good description of any underlying dynamics, such as the description of modulated waves in deep water or nonlinear optics. In those cases, the decomposition of experimental data requires fewer modes compared to regular Fourier analysis, and the truncated components remain unimportant on longer time scales.