Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane

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Show simple item record Deaño Cabrera, Alfredo 2021-02-23T13:08:39Z 2021-02-23T13:08:39Z 2018-10-03
dc.identifier.bibliographicCitation SIGMA, (2018), v.14, 107, [19] p.
dc.identifier.issn 1815-0659
dc.description This paper is a contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev. The full collection is available at
dc.description.abstract In this paper we obtain large z asymptotic expansions in the complex plane forthe tau function corresponding to special function solutions of the Painlevé II differentialequation. Using the fact that these tau functions can be written as n × n Wronskiandeterminants involving classical Airy functions, we use Heine's formula to rewrite them asn-fold integrals, which can be asymptotically approximated using the classical method ofsteepest descent in the complex plane.
dc.description.sponsorship The author acknowledges financial support from the EPSRC grant "Painlevé equations: analytical properties and numerical computation", reference EP/P026532/1, and from the project MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitivity. The author wishes to thank M. Fasondini, D. Huybrechs, A. Iserles, A.R. Its, A.B.J. Kuijlaars, A.F. Loureiro, C. Pechand W. Van Assche for stimulating discussions on the topic and scope of this paper, as well as the organisers of the workshop "Painlevé Equations and Applications" held at the University of Michigan, August 25-29, 2017, for their hospitality. The comments, remarks and corrections of the anonymous referees have lead to an improved version of the paper, and they are greatly appreciated.
dc.format.extent 19
dc.language.iso eng
dc.publisher Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine
dc.rights The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Painlevé equations
dc.subject.other Asymptotic expansions
dc.subject.other Airy functions
dc.title Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2015-65888-C4-2-P
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 107
dc.identifier.publicationlastpage 19
dc.identifier.publicationtitle Symmetry Integrability and Geometry: Methods and Applications
dc.identifier.publicationvolume 14
dc.identifier.uxxi AR/0000026483
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Análisis Aplicado
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