Justification of the NLS Approximation for the Euler-Poisson Equation

被引：12
作者：
Liu, Huimin [1 ]
Pu, Xueke [2 ]
机构：
[1] Shanxi Univ Finance & Econ, Fac Appl Math, Taiyuan 030006, Shanxi, Peoples R China
[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2019年 / 371卷 / 02期
基金：
中国国家自然科学基金;
关键词：
WATER-WAVE PROBLEM; KORTEWEG-DE-VRIES; MODULATION APPROXIMATION; SYSTEM; LIMIT; VALIDITY;
D O I：
10.1007/s00220-019-03576-4
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The nonlinear Schrodinger (NLS) equation can be derived as a formal approximation equation describing the envelopes of slowly modulated spatially and temporarily oscillating wave packet-like solutions to the ion Euler-Poisson equation. In this paper, we rigorously justify such approximation by giving error estimates in Sobolev norms between exact solutions of the ion Euler-Poisson system and the formal approximation obtained via the NLS equation. The justification consists of several difficulties such as the resonances and loss of regularity, due to the quasilinearity of the problem. These difficulties are overcome by introducing normal form transformation and cutoff functions and carefully constructed energy functional of the equation.
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页码：357 / 398
页数：42
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