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

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

Autor(es): Deaño Cabrera, Alfredo
Editorial: Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine
Fecha de edición: 2018-10-03
Cita: SIGMA, (2018), v.14, 107, [19] p.
ISSN: 1815-0659
DOI: https://doi.org/10.3842/SIGMA.2018.107
Patrocinador: Ministerio de Economía y Competitividad (España)
Agradecimientos: 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.
Proyecto: Gobierno de España. MTM2015-65888-C4-2-P
Palabras clave: Painlevé equations , Asymptotic expansions , Airy functions
URI: http://hdl.handle.net/10016/32004
Derechos: The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License
Atribución-NoComercial-SinDerivadas 3.0 España
The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License

Resumen:

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 Wronskiandetermi [+]

Nota:

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

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