一种证明导数NLS近似的鲁棒方法

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Zeitschrift fur Angewandte Mathematik und Physik 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

Zeitschrift fur Angewandte Mathematik und Physik 数学-应用数学

CiteScore

2.90

自引率

10.00%

发文量

216

审稿时长

6-12 weeks

期刊介绍： The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.