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.

On an isomonodromy deformation equation without the Painlevé property

Dubrovin, Boris;Kapaev, Andrei
2014-01-01

Abstract

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.
2014
21
1
9
35
https://arxiv.org/abs/1301.7211
Dubrovin, Boris; Kapaev, Andrei
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11755
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