Nonlinear Schrödinger Approximation for the Electron Euler-Poisson Equation
Nonlinear Schrödinger Approximation for the Electron Euler-Poisson Equation
复制标题
电子欧拉-泊松方程的非线性薛定谔近似
DOI：
10.1007/s11401-023-0020-2
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Xueke Pu
中科院分区：
文献类型：
--
作者：
Huimin Liu;Xueke Pu
非线性薛定谔（NLS）方程在描述波包在时间和空间上的慢调制中起着重要的作用。本文研究了描述等离子体中朗缪尔波的一个重要模型--电子Euler-Poisson方程的NLS近似，在Sobolev空间中给出了严格的误差估计。他们通过多尺度分析得到了演化方程的近似波包解，然后构造了基于二次项的修正能量泛函，并利用旋转坐标变换得到了近似解与真实解之间误差的统一估计。
The nonlinear Schrödinger (NLS for short) equation plays an important role in describing slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet. In this paper, the authors study the NLS approximation by providing rigorous error estimates in Sobolev spaces for the electron Euler-Poisson equation, an important model to describe Langmuir waves in a plasma. They derive an approximate wave packet-like solution to the evolution equations by the multiscale analysis, then they construct the modified energy functional based on the quadratic terms and use the rotating coordinate transform to obtain uniform estimates of the error between the true and approximate solutions.