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dc.creatorFerreira González, Cheloes_ES
dc.creatorLópez García, José Luises_ES
dc.creatorPérez Sinusía, Esteres_ES
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.format.extent15 p.
dc.relation.ispartofApplied Mathematics and Computation 339 (2018) 837–845en
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.subjectSwallowtail integralen
dc.subjectAsymptotic expansionsen
dc.subjectModified saddle point methoden
dc.titleThe asymptotic expansion of the swallowtail integral in the highly oscillatory regionen
dc.typeArtículo / Artikuluaes
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.rights.accessRightsAcceso abierto / Sarbide irekiaes
dc.type.versionVersión aceptada / Onetsi den bertsioaes
dc.contributor.funderUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoaes

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© 2018 Elsevier Inc. All rights reserved. The manuscript version is made available under the CC BY-NC-ND 4.0 license.
Except where otherwise noted, this item's license is described as © 2018 Elsevier Inc. All rights reserved. The manuscript version is made available under the CC BY-NC-ND 4.0 license.

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