Error estimates for Gaussian beams at a fold caustic

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2023-10-06 DOI:10.3233/asy-231852

Olivier Lafitte, Olof Runborg

引用次数: 0

Abstract

In this work we show an error estimate for a first order Gaussian beam at a fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For the caustic that we study the exact solution can be constructed using Airy functions and there are explicit formulae for the Gaussian beam parameters. Via precise comparisons we show that the pointwise error on the caustic is of the order O ( k − 5 / 6 ) where k is the wave number in Helmholtz.

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高斯光束在二次焦散处的误差估计

在这项工作中，我们展示了一阶高斯光束在一个折叠焦散点上的误差估计，近似于由亥姆霍兹方程控制的时间谐波。对于我们所研究的焦散，精确解可以用Airy函数构造，高斯光束参数有明确的表达式。通过精确的比较，我们发现焦散上的点向误差为O (k−5 / 6)阶，其中k为亥姆霍兹波数。

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

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.