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

Deaño Cabrera, Alfredo

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

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Análisis Aplicado	es
dc.contributor.author	Deaño Cabrera, Alfredo
dc.contributor.funder	Ministerio de Economía y Competitividad (España)	es
dc.date.accessioned	2021-02-23T13:08:39Z
dc.date.available	2021-02-23T13:08:39Z
dc.date.issued	2018-10-03
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	en
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.	en
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.	en
dc.description.status	Publicado	es
dc.format.extent	19
dc.identifier.bibliographicCitation	SIGMA, (2018), v.14, 107, [19] p.	en
dc.identifier.doi	https://doi.org/10.3842/SIGMA.2018.107
dc.identifier.issn	1815-0659
dc.identifier.publicationfirstpage	1
dc.identifier.publicationissue	107
dc.identifier.publicationlastpage	19
dc.identifier.publicationtitle	Symmetry Integrability and Geometry: Methods and Applications	en
dc.identifier.publicationvolume	14	es
dc.identifier.uri	https://hdl.handle.net/10016/32004
dc.identifier.uxxi	AR/0000026483
dc.language.iso	eng	en
dc.publisher	Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine	en
dc.relation.projectID	Gobierno de España. MTM2015-65888-C4-2-P	es
dc.rights	The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Painlevé equations	en
dc.subject.other	Asymptotic expansions	en
dc.subject.other	Airy functions	en
dc.title	Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane	en
dc.type	research article	*
dc.type.hasVersion	VoR	*
dspace.entity.type	Publication