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Classical solutions of the Degenerate Fifth Painlevé Equation

Clarkson, Peter (2023) Classical solutions of the Degenerate Fifth Painlevé Equation. Journal of Physics A: Mathematical and Theoretical, 56 (13). Article Number 134002. ISSN 1751-8113. E-ISSN 1751-8121. (doi:10.1088/1751-8121/acbef1) (KAR id:100232)

Abstract

In this paper classical solutions of the degenerate fifth Painlevé equation are classified, which include hierarchies of algebraic solutions and solutions expressible in terms of Bessel functions. Solutions of the degenerate fifth Painlevé equation are known to expressible in terms of the third Painlevé equation. Here the classification and description of the classical solutions of the degenerate fifth Painlevé equation are done directly, than through the third Painlevé equation. Two applications of these classical solutions are discussed, deriving exact solutions of the complex sine-Gordon equation and of the coefficients in the three-term recurrence relation associated with generalised Charlier polynomials.

Item Type: Article
DOI/Identification number: 10.1088/1751-8121/acbef1
Uncontrolled keywords: Painlevé equation, Bessel functions, Rational solutions, complex sine-Gordon equation, generalised Charlier polynoimals
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: University of Kent (https://ror.org/00xkeyj56)
Depositing User: Peter Clarkson
Date Deposited: 27 Feb 2023 10:42 UTC
Last Modified: 24 Feb 2024 00:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/100232 (The current URI for this page, for reference purposes)

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