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.
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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.
|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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