A robust way to justify the derivative NLS approximation

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

引用次数: 1

Abstract

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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一种证明导数NLS近似的鲁棒方法

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。

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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

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