TY - JOUR
T1 - On an isomonodromy deformation equation without the PainlevĂ© property
Y1 - 2014
A1 - Boris Dubrovin
A1 - Andrey Kapaev
AB - 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.
PB - Maik Nauka-Interperiodica Publishing
UR - http://hdl.handle.net/1963/6466
N1 - 34 pages, 8 figures, references added
U1 - 6410
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -