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 |
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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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Marco Fasondini |
Date Deposited: | 13 Mar 2018 18:28 UTC |
Last Modified: | 04 Mar 2024 17:46 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/66369 (The current URI for this page, for reference purposes) |
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