The Lax pair for the mKdV hierarchy

Clarkson, Peter and Joshi, Nalini and Mazzocco, M. (2006) The Lax pair for the mKdV hierarchy. In: Delabaere, Eric and Loday-Richaud, Michele, eds. Théories Asymptotiques et Equations de Painlevé. Séminaires et Congrès (14). Sociètè Mathèematique de France, Paris, France, pp. 53-64. ISBN 978-2-85629-229-7. (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:3223)

 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.

Abstract

Rational solutions of the second, third and fourth Painlevé equations (-) can be expressed in terms of logarithmic derivatives of special polynomials that are defined through coupled second order, bilinear differential-difference equations which are equivalent to the Toda equation.

In this paper the structure of the roots of these special polynomials, and the special polynomials associated with algebraic solutions of the third and fifth Painlevé equations, is studied and it is shown that these have an intriguing, highly symmetric and regular structure. Further, using the Hamiltonian theory for -, it is shown that all these special polynomials, which are defined by differential-difference equations, also satisfy fourth order, bilinear ordinary differential equations.

Item Type: Book section Hamiltonians, Painlevé equations, rational solutions Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Peter Clarkson 07 Jun 2008 11:54 UTC 16 Nov 2021 09:41 UTC https://kar.kent.ac.uk/id/eprint/3223 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-8777-5284