论文标题
周期性NLS的傅立叶集成符：通过离散的波尔加恩空间的低规律性估计
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
论文作者
论文摘要
在本文中，我们提出了一种新的方案，用于整合周期性的非线性schrödinger方程，并严格证明以低规律性的方式证明收敛速率。新的集成商比规律性低的标准方案具有决定性的优势。特别是，它能够以$ 0 <s \ le 1 $处理$ h^s $中的初始数据。集成商的关键特征是它能够区分解决方案中的低和中频，并在离散化中对其进行不同的处理。这种新方法需要一个均衡的过滤过程，该过程在傅立叶空间中进行。提出的方案的收敛分析基于我们在本文中介绍的离散（及时）波尔加因空间估计。数值实验说明了新集成商比标准方案的优越性对于粗略的初始数据。
In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low regularity. In particular, it is able to handle initial data in $H^s$ for $0 < s\le 1$. The key feature of the integrator is its ability to distinguish between low and medium frequencies in the solution and to treat them differently in the discretization. This new approach requires a well-balanced filtering procedure which is carried out in Fourier space. The convergence analysis of the proposed scheme is based on discrete (in time) Bourgain space estimates which we introduce in this paper. A numerical experiment illustrates the superiority of the new integrator over standard schemes for rough initial data.
