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

dc.contributor.authorFerreira González, Chelo
dc.contributor.authorLópez García, José Luis
dc.contributor.authorPérez Sinusía, Ester
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.contributor.funderUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoaes
dc.date.accessioned2018-12-14T12:04:17Z
dc.date.available2020-12-15T00:00:13Z
dc.date.issued2018
dc.description.abstractThe mathematical models of many short wavelength phenomena, specially wave propagation and optical diffraction, contain, as a basic ingredient, oscillatory integrals with several nearly coincident stationary phase or saddle points. The uniform approximation of those integrals can be expressed in terms of certain canonical integrals and their derivatives [2,16]. The importance of these canonical diffraction integrals is stressed in [14] by means of the following sentence: The role played by these canonical diffraction integrals in the analysis of caustic wave fields is analogous to that played by complex exponentials in plane wave theory. Apart from their mathematical importance in the uniform asymptotic approximation of oscillatory integrals [12], the canonical diffraction integrals have physical applications in the description of surface gravity waves [11], [17], bifurcation sets, optics, quantum mechanics, chemical physics [4] and acoustics (see [1], Section 36.14 and references there in). To our knowledge, the first application of this family of integrals traces back to the description of the disturbances on a water surface produced, for example, by a traveling ship. These disturbances form a familiar pattern of bow and stern waves which was first explained mathematically by Lord Kelvin [10] using these integrals.en
dc.description.sponsorshipThis research was supported by the Ministerio de Economía y Competitividad (MTM2014-52859) and the Universidad Pública de Navarra.en
dc.embargo.lift2020-12-15
dc.embargo.terms2020-12-15
dc.format.extent15 p.
dc.format.mimetypeapplication/pdfen
dc.identifier.doi10.1016/j.amc.2018.07.008
dc.identifier.issn0096-3003
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/31780
dc.language.isoengen
dc.publisherElsevieren
dc.relation.ispartofApplied Mathematics and Computation 339 (2018) 837–845en
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/en
dc.relation.publisherversionhttps://doi.org/10.1016/j.amc.2018.07.008
dc.rights© 2018 Elsevier Inc. All rights reserved. The manuscript version is made available under the CC BY-NC-ND 4.0 license.en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectSwallowtail integralen
dc.subjectAsymptotic expansionsen
dc.subjectModified saddle point methoden
dc.titleThe asymptotic expansion of the swallowtail integral in the highly oscillatory regionen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersionen
dc.type.versionVersión aceptada / Onetsi den bertsioaes
dspace.entity.typePublication
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relation.isAuthorOfPublicatione6cd33c5-6d5e-455c-b8da-32a9702e16c8
relation.isAuthorOfPublication93f891c7-529d-4972-8759-9d943c60949c
relation.isAuthorOfPublication.latestForDiscovery8b28fd50-66f4-431e-a219-43d8c02bb077

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