Error estimates for Gaussian beams at a fold caustic

DOI10.3233/ASY-231852zbMath1528.35178arXiv2304.00556OpenAlexW4323066022MaRDI QIDQ6070628

Olivier Lafitte, Olof Runborg

Publication date: 23 November 2023

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.00556

zbMATH Keywords

error estimatescausticsGaussian beamshigh frequency wave asymptotics

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Waves and radiation in optics and electromagnetic theory (78A40) Asymptotic analysis in optics and electromagnetic theory (78M35) Geometric optics (78A05)

Cites Work

• Unnamed Item
• Sobolev and max norm error estimates for Gaussian beam superpositions
• The band spectrum of the periodic Airy-Schrödinger operator on the real line
• Gaussian Beam Methods for the Helmholtz Equation
• Error estimates for Gaussian beam superpositions
• General superpositions of Gaussian beams and propagation errors
• Optimal Error Estimates for First-Order Gaussian Beam Approximations to the Schrödinger Equation
• Uniform asymptotic expansions at a caustic

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