%0 Journal Article
%D 2014
%T On an isomonodromy deformation equation without the PainlevĂ© property
%A Boris Dubrovin
%A Andrey Kapaev
%X 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.
%I Maik Nauka-Interperiodica Publishing
%G en
%U http://hdl.handle.net/1963/6466
%1 6410
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:29:56Z
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%R 10.1134/S1061920814010026