Application of the isomonodromy deformation method to the fourth Painleve equation

Milne, A.E. and Clarkson, P.A. and Bassom, A.P. (1997) Application of the isomonodromy deformation method to the fourth Painleve equation. Inverse Problems, 13 (2). pp. 421-439. ISSN 0266-5611. (The full text of this publication is not available from this repository)

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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
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: M.A. Ziai
Date Deposited: 18 Apr 2009 18:49
Last Modified: 18 Apr 2009 18:49
Resource URI: http://kar.kent.ac.uk/id/eprint/18191 (The current URI for this page, for reference purposes)
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