On an isomonodromy deformation equation without the Painlevé property

We show that the fourth-order nonlinear ODE which controls the pole dynamics in the general solution of equation PI2 compatible with the KdV equation exhibits two remarkable properties: (1) it governs the isomonodromy deformations of a 2 × 2 matrix linear ODE with polynomial coefficients, and (2) it does not possess the Painlevé property. We also study the properties of the Riemann-Hilbert problem associated to this ODE and find its large-t asymptotic solution for physically interesting initial data. © 2014 Pleiades Publishing, Ltd.