The Pearcey integral in the highly oscillatory region II

We consider the Pearcey integral P(x, y) for large values of |x| and bounded values of |y|. The standard saddle point analysis is difficult to apply because the Pearcey integral is highly oscillating in this region. To overcome this problem we use the modified saddle point method introduced in López...

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Autores: Ferreira González, Chelo, López García, José Luis, Pérez Sinusía, Ester
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Recursos:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/54377
Acesso em linha:https://hdl.handle.net/2454/54377
Access Level:acceso abierto
Palavra-chave:Pearcey integral
Asymptotic expansions
Simplified saddle point method
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spelling The Pearcey integral in the highly oscillatory region IIFerreira González, CheloLópez García, José LuisPérez Sinusía, EsterPearcey integralAsymptotic expansionsSimplified saddle point methodWe consider the Pearcey integral P(x, y) for large values of |x| and bounded values of |y|. The standard saddle point analysis is difficult to apply because the Pearcey integral is highly oscillating in this region. To overcome this problem we use the modified saddle point method introduced in López et al. (2009). A complete asymptotic analysis is possible with this method, and we derive a complete asymptotic expansion of P(x, y) for large |x|, accompanied by the exact location of the Stokes lines. There are two Stokes lines that divide the complex x−plane in two different sectors in which P(x, y) behaves differently when |x| is large. The asymptotic approximation is the sum of two asymptotic series whose terms are elementary functions of x and y. Both of them are of Poincaré type; one of them is given in terms of inverse powers of x; the other one in terms of inverse powers of x 1/2 , and it is multiplied by an exponential factor that behaves differently in the two mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation.This research was supported by the Spanish Ministerio de Ciencia, Innovación y Universidades, project PID2022-136441NB-I00.ElsevierEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT22025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/54377reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00© 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license.http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/543772026-06-17T12:41:47Z
dc.title.none.fl_str_mv The Pearcey integral in the highly oscillatory region II
title The Pearcey integral in the highly oscillatory region II
spellingShingle The Pearcey integral in the highly oscillatory region II
Ferreira González, Chelo
Pearcey integral
Asymptotic expansions
Simplified saddle point method
title_short The Pearcey integral in the highly oscillatory region II
title_full The Pearcey integral in the highly oscillatory region II
title_fullStr The Pearcey integral in the highly oscillatory region II
title_full_unstemmed The Pearcey integral in the highly oscillatory region II
title_sort The Pearcey integral in the highly oscillatory region II
dc.creator.none.fl_str_mv Ferreira González, Chelo
López García, José Luis
Pérez Sinusía, Ester
author Ferreira González, Chelo
author_facet Ferreira González, Chelo
López García, José Luis
Pérez Sinusía, Ester
author_role author
author2 López García, José Luis
Pérez Sinusía, Ester
author2_role author
author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
dc.subject.none.fl_str_mv Pearcey integral
Asymptotic expansions
Simplified saddle point method
topic Pearcey integral
Asymptotic expansions
Simplified saddle point method
description We consider the Pearcey integral P(x, y) for large values of |x| and bounded values of |y|. The standard saddle point analysis is difficult to apply because the Pearcey integral is highly oscillating in this region. To overcome this problem we use the modified saddle point method introduced in López et al. (2009). A complete asymptotic analysis is possible with this method, and we derive a complete asymptotic expansion of P(x, y) for large |x|, accompanied by the exact location of the Stokes lines. There are two Stokes lines that divide the complex x−plane in two different sectors in which P(x, y) behaves differently when |x| is large. The asymptotic approximation is the sum of two asymptotic series whose terms are elementary functions of x and y. Both of them are of Poincaré type; one of them is given in terms of inverse powers of x; the other one in terms of inverse powers of x 1/2 , and it is multiplied by an exponential factor that behaves differently in the two mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/54377
url https://hdl.handle.net/2454/54377
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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