The third Painlevé equation and associated special polynomials

Clarkson, Peter (2003) The third Painlevé equation and associated special polynomials. Journal of Physics A: Mathematical and General, 36 (36). pp. 9507-9532. ISSN 0305-4470. (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)

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In this paper we are concerned with rational solutions, algebraic solutions and associated special polynomials with these solutions for the third Painlevé equation (PIII). These rational and algebraic solutions of PIII are expressible in terms of special polynomials defined by second-order, bilinear differential-difference equations which are equivalent to Toda equations. The structure of the roots of these special polynomials is studied and it is shown that these have an intriguing, highly symmetric and regular structure. Using the Hamiltonian theory for PIII, it is shown that these special polynomials satisfy pure difference equations, fourth-order, bilinear differential equations as well as differential-difference equations. Further, representations of the associated rational solutions in the form of determinants through Schur functions are given.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Peter A Clarkson
Date Deposited: 06 Jun 2008 13:06
Last Modified: 29 Apr 2014 14:14
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