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A computational exploration of the McCoy–Tracy–Wu solutions of the third Painlevé equation

Fasondini, Marco, Fornberg, Bengt, Weideman, J.A.C. (2018) A computational exploration of the McCoy–Tracy–Wu solutions of the third Painlevé equation. Physica D: Nonlinear Phenomena, 363 . pp. 18-43. ISSN 0167-2789. (doi:10.1016/j.physd.2017.10.011) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:66369)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
https://dx.doi.org/10.1016/j.physd.2017.10.011

Abstract

The method recently developed by the authors for the computation of the multivalued Painlevé transcendents on their Riemann surfaces (Fasondini et al., 2017) is used to explore families of solutions to the third Painlevé equation that were identified by McCoy et al. (1977) and which contain a pole-free sector. Limiting cases, in which the solutions are singular functions of the parameters, are also investigated and it is shown that a particular set of limiting solutions is expressible in terms of special functions. Solutions that are single-valued, logarithmically (infinitely) branched and algebraically branched, with any number of distinct sheets, are encountered. The algebraically branched solutions have multiple pole-free sectors on their Riemann surfaces that are accounted for by using asymptotic formulae and Bäcklund transformations.

Item Type: Article
DOI/Identification number: 10.1016/j.physd.2017.10.011
Uncontrolled keywords: Painlevé transcendents, PIII, equation, Tronquée solutions, Connection formulae, Bäcklund transformations, Pole field solver
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Marco Fasondini
Date Deposited: 13 Mar 2018 18:28 UTC
Last Modified: 13 Jan 2020 10:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/66369 (The current URI for this page, for reference purposes)
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