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Application of the isomonodromy deformation method to the fourth Painleve equation

Milne, Alice E., Clarkson, Peter, Bassom, Andrew P. (1997) Application of the isomonodromy deformation method to the fourth Painleve equation. Inverse Problems, 13 (2). pp. 421-439. ISSN 0266-5611. (doi:10.1088/0266-5611/13/2/015) (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:18191)

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/10.1088/0266-5611/13/2/015

Abstract

In this paper we study the fourth Painleve equation and how the concept of isomonodromy may be used to elucidate properties of its solutions. This work is based on a Lax pair which is derived from an inverse scattering formalism for a derivative nonlinear Schrodinger system, which in turn possesses a symmetry reduction that reduces it to the fourth Painleve equation. It is shown how the monodromy data of our Lax pair can be explicitly computed in a number of cases and the relationships between special solutions of the monodromy equations and particular integrals of the fourth PainlevB equation are discussed. We use a gauge transformation technique to derive Backlund transformations from our Lax pair and generalize the findings to examine particular solutions and Backlund transformations of a related nonlinear harmonic oscillator equation.

Item Type: Article
DOI/Identification number: 10.1088/0266-5611/13/2/015
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: M.A. Ziai
Date Deposited: 18 Apr 2009 18:49 UTC
Last Modified: 16 Nov 2021 09:56 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/18191 (The current URI for this page, for reference purposes)

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