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

Deaño Cabrera, Alfredo

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dc.contributor.author	Deaño Cabrera, Alfredo
dc.date.accessioned	2021-02-23T13:08:39Z
dc.date.available	2021-02-23T13:08:39Z
dc.date.issued	2018-10-03
dc.identifier.bibliographicCitation	SIGMA, (2018), v.14, 107, [19] p.
dc.identifier.issn	1815-0659
dc.identifier.uri	http://hdl.handle.net/10016/32004
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 https://www.emis.de/journals/SIGMA/Kapaev.html
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.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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.identifier.doi	https://doi.org/10.3842/SIGMA.2018.107
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