APPLICATION OF THE ISOMONODROMY DEFORMATION METHOD TO THE 4TH PAINLEVE EQUATION

In this paper we study the fourth Painleve equation and how the concep t 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 sc attering formalism for a derivative nonlinear Schrodinger system, whic h 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 i ntegrals 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 a nd Backlund transformations of a related nonlinear harmonic oscillator equation.