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Remarks on the Yablonskii–Vorob'ev polynomials

Clarkson, Peter (2003) Remarks on the Yablonskii–Vorob'ev polynomials. Physics Letters A, 319 (1-2). pp. 137-144. ISSN 0375-9601. (doi:10.1016/j.physleta.2003.10.016) (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:3247)

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.physleta.2003.10.016

Abstract

It is well known that rational solutions of the second Painlevé equation (PII) are expressed in terms of logarithmic derivatives of the Yablonskii–Vorob'ev polynomials Qn(z) which are defined through a second order, bilinear differential-difference equation which is equivalent to the Toda equation. In this Letter, using the Hamiltonian theory for PII, it is shown that Qn(z) also satisfies a fourth order, bilinear ordinary differential equation and a fifth order, quad-linear difference equation. Further, rational solutions of some ordinary differential equations which are solvable in terms of solutions of PII are also expressed in terms of the Yablonskii–Vorob'ev polynomials.

Item Type: Article
DOI/Identification number: 10.1016/j.physleta.2003.10.016
Uncontrolled keywords: painleve equations; Yablonskii-Vorob'ev polynomials
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 10:40 UTC
Last Modified: 16 Nov 2021 09:41 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/3247 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
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