Darboux transformations and the symmetric fourth Painlevé equation

Sen, A. and Hone, Andrew N.W. and Clarkson, Peter (2005) Darboux transformations and the symmetric fourth Painlevé equation. Journal of Physics A: Mathematical and General, 38 (45). pp. 9751-9764. ISSN 0305-4470. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1088/0305-4470/38/45/003

Abstract

This paper is concerned with the group symmetries of the fourth Painleve equation P-IV, a second-order nonlinear ordinary differential equation. It is well known that the parameter space of P-IV admits the action of the extended affine Weyl group A(2)((1)). As shown by Noumi and Yamada, the action of A(2)((1)) as Backlund transformations of P-IV provides a derivation of its symmetric form SP4. The dynamical System SP4 is also equivalent to the isomonodromic deformation of an associated three-by-three matrix linear system (Lax pair). The action of the generators of A(2)((1)) on this Lax pair is derived using the Darboux transformation for an associated third-order operator

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: Andrew N W Hone
Date Deposited: 06 Jun 2008 11:39
Last Modified: 23 Jun 2014 08:41
Resource URI: http://kar.kent.ac.uk/id/eprint/3250 (The current URI for this page, for reference purposes)
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