On an isomonodromy deformation equation without the Painlevé property

Abstract

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 $2\times 2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses 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 the physically interesting initial data.

34 pages, 8 figures, references added

References in corpus (1)

• Affine Weyl group approach to Painlevé equations

Cited by in corpus (6)

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• Systematic construction of non-autonomous Hamiltonian equations of Painlevé-type. I. Frobenius integrability
• Non-autonomous Henon-Heiles system from Painleve class
• Tronquée Solutions of the Third and Fourth Painlevé Equations
• On the tritronquée solutions of P${}_I^2$
• Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type