Backlund transformations for the second Painleve hierarchy: a modified truncation approach

Clarkson, Peter and Joshi, Nalini and Pickering, Andrew (1999) Backlund transformations for the second Painleve hierarchy: a modified truncation approach. Inverse Problems, 15 (1). pp. 175-187. ISSN 0266-5611. (doi:https://doi.org/10.1088/0266-5611/15/1/019) (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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Official URL http://dx.doi.org/10.1088/0266-5611/15/1/019

Abstract

The second Painleve hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well known second Painleve equation, P-11. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painleve analysis to ordinary differential equations. We extend these techniques in order to derive auto-Backlund transformations for the second Painleve hierarchy. We also derive a number of other Backlund transformations, including a Backlund transformation onto a hierarchy of P-34 equations, and a little known Backlund transformation for P-11 itself. We then use our results on Backlund transformations to obtain, for each member of the P-11 hierarchy, a sequence of special integrals.

Item Type:	Article
Subjects:	Q Science > QA Mathematics (inc Computing science)
Divisions:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User:	M. Nasiriavanaki
Date Deposited:	25 Jun 2009 07:38 UTC
Last Modified:	28 Apr 2014 13:24 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/17219 (The current URI for this page, for reference purposes)