Publication: The asymptotic expansion of the swallowtail integral in the highly oscillatory region
| dc.contributor.author | Ferreira González, Chelo | |
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Pérez Sinusía, Ester | |
| dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
| dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa | es |
| dc.date.accessioned | 2018-12-14T12:04:17Z | |
| dc.date.available | 2020-12-15T00:00:13Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | The 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.sponsorship | This research was supported by the Ministerio de Economía y Competitividad (MTM2014-52859) and the Universidad Pública de Navarra. | en |
| dc.embargo.lift | 2020-12-15 | |
| dc.embargo.terms | 2020-12-15 | |
| dc.format.extent | 15 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1016/j.amc.2018.07.008 | |
| dc.identifier.issn | 0096-3003 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/31780 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | Applied Mathematics and Computation 339 (2018) 837–845 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/ | en |
| dc.relation.publisherversion | https://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.accessRights | info:eu-repo/semantics/openAccess | en |
| dc.rights.accessRights | Acceso abierto / Sarbide irekia | es |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Swallowtail integral | en |
| dc.subject | Asymptotic expansions | en |
| dc.subject | Modified saddle point method | en |
| dc.title | The asymptotic expansion of the swallowtail integral in the highly oscillatory region | en |
| dc.type | info:eu-repo/semantics/article | en |
| dc.type | Artículo / Artikulua | es |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
| dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b28fd50-66f4-431e-a219-43d8c02bb077 | |
| relation.isAuthorOfPublication | e6cd33c5-6d5e-455c-b8da-32a9702e16c8 | |
| relation.isAuthorOfPublication | 93f891c7-529d-4972-8759-9d943c60949c | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b28fd50-66f4-431e-a219-43d8c02bb077 |