On an Isomonodromy Deformation Equation without the Painlevé Property
نویسنده
چکیده
Abstract. We show that the fourth-order nonlinear ODE which controls the pole dynamics in the general solution of equation P 2 I 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.
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