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Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

Fasondini, Marco, Fornberg, Bengt, Weideman, J.A.C. (2017) Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces. Journal of Computational Physics, 344 . pp. 36-50. ISSN 0021-9991. (doi:10.1016/j.jcp.2017.04.071) (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:66319)

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
http://dx.doi.org/10.1016/j.jcp.2017.04.071

Abstract

We extend the numerical pole field solver (Fornberg and Weideman (2011) [12]) to enable the computation of the multivalued Painlevé transcendents, which are the solutions to the third, fifth and sixth Painlevé equations, on their Riemann surfaces. We display, for the first time, solutions to these equations on multiple Riemann sheets. We also provide numerical evidence for the existence of solutions to the sixth Painlevé equation that have pole-free sectors, known as tronquée solutions.

Item Type: Article
DOI/Identification number: 10.1016/j.jcp.2017.04.071
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QC Physics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Marco Fasondini
Date Deposited: 08 Mar 2018 13:10 UTC
Last Modified: 13 Jan 2020 10:51 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/66319 (The current URI for this page, for reference purposes)
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