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Special polynomials associated with rational solutions of the fifth Painlevé equation

Clarkson, Peter (2005) Special polynomials associated with rational solutions of the fifth Painlevé equation. Journal of Computational and Applied Mathematics, 178 (1-2). pp. 111-129. ISSN 0377-0427. (doi:10.1016/j.cam.2004.04.015) (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:3246)

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.
Official URL:
http://dx.doi.org/10.1016/j.cam.2004.04.015

Abstract

In this paper special polynomials associated with rational and algebraic solutions of the fifth Painlevéequation (PV) are studied. These special polynomials defined by second-order, bilinear differential-difference equations which are equivalent to Toda equations. The structure of the zeroes of these special polynomials, which involve a parameter, is investigated and it is shown that these have an intriguing, symmetric and regular structure. For large negative values of the parameter the zeroes have an approximate triangular structure. As the parameter increases the zeroes coalesce for certain values and eventually for large positive values of the parameter the zeroes also have an approximate triangular structure, though with the orientation reversed. In fact, the interaction of the zeroes is “solitonic” in nature since the same pattern reappears, with its orientation reversed.

Item Type: Article
DOI/Identification number: 10.1016/j.cam.2004.04.015
Uncontrolled keywords: Painleve equations; rational solutions; Toda equations
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: Peter Clarkson
Date Deposited: 06 Jun 2008 10:26 UTC
Last Modified: 16 Nov 2021 09:41 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/3246 (The current URI for this page, for reference purposes)

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