1301.7211 (Boris Dubrovin et al.)

On an isomonodromy deformation equation without the Painlevé property    [PDF]

Boris Dubrovin, Andrei Kapaev

We show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1)~it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2)~it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data.

View original: http://arxiv.org/abs/1301.7211