Error estimates for Gaussian beams at a fold caustic
Classical Analysis and ODEs
2023-07-18 v2 Numerical Analysis
Analysis of PDEs
Numerical Analysis
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 where is the wave number in Helmholtz.
Cite
@article{arxiv.2304.00556,
title = {Error estimates for Gaussian beams at a fold caustic},
author = {Olivier Lafitte and Olof Runborg},
journal= {arXiv preprint arXiv:2304.00556},
year = {2023}
}