The asymptotic expansion of the swallowtail integral in the highly oscillatory region

DOI10.1016/j.amc.2018.07.008zbMath1428.33042OpenAlexW2888270039WikidataQ129335731 ScholiaQ129335731MaRDI QIDQ2007597

Ester Pérez Sinusía, Chelo Ferreira, José Luis López

Publication date: 22 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/2454/31780

zbMATH Keywords

asymptotic expansionsmodified saddle point methodswallowtail integral

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions defined by series and integrals (33E20)

Related Items (6)

The swallowtail integral in the highly oscillatory region III ⋮ Controlling the Trajectory of Swallowtail Gaussian Beams in Dynamic Parabolic Potentials ⋮ Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals ⋮ An asymptotic expansion of the hyberbolic umbilic catastrophe integral ⋮ Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis ⋮ The swallowtail integral in the highly oscillatory region. II

Uses Software

• DLMF

Cites Work

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• The Pearcey integral in the highly oscillatory region
• Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions
• A systematization of the saddle point method. Application to the Airy and Hankel functions
• On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles
• Convergent and asymptotic expansions of the Pearcey integral
• Asymptotic Expansion of the Pearcey Integral Near the Caustic
• A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: application to Pearcey's integral and its derivatives
• The asymptotic behaviour of Pearcey’s integral for complex variables
• Asymptotics of the Swallowtail Integral Near the Cusp of the Caustic

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