一种证明导数NLS近似的鲁棒方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-14 DOI:10.1007/s00033-023-02121-7

Max Heß, Guido Schneider

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引用次数: 1

摘要

摘要通过多尺度摄动分析，可以将微分非线性Schrödinger (DNLS)方程导出为振幅方程，用于描述色散波系统中底层振荡和行波包的慢变化包络。当类似导出的NLS方程的三次系数消失时，出现退化情况。本文的目的是证明DNLS近似在原色散波系统较弱的假设下，如果假定DNLS方程的初始条件在复平面上是解析的，则DNLS近似能正确地预测原系统的动力学。针对具有三次非线性的Klein-Gordon模型，提出了该方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A robust way to justify the derivative NLS approximation

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A robust way to justify the derivative NLS approximation

Abstract The derivative nonlinear Schrödinger (DNLS) equation can be derived as an amplitude equation via multiple scaling perturbation analysis for the description of the slowly varying envelope of an underlying oscillating and traveling wave packet in dispersive wave systems. It appears in the degenerated situation when the cubic coefficient of the similarly derived NLS equation vanishes. It is the purpose of this paper to prove that the DNLS approximation makes correct predictions about the dynamics of the original system under rather weak assumptions on the original dispersive wave system if we assume that the initial conditions of the DNLS equation are analytic in a strip of the complex plane. The method is presented for a Klein–Gordon model with a cubic nonlinearity.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.