THE METHOD OF ISOMONODROMY DEFORMATIONS AND CONNECTION FORMULAS FOR THE SECOND PAINLEVÉ TRANSCENDENT

A complete asymptotic description is given for the general real solution of the second Painleve equation, , including explicit formulas connecting the asymptotics as . The approach is based on the asymptotic solution of the direct problem of monodromy theory for a linear system associated with the Painleve equation in the framework of the method of isomonodromy deformations. There is a brief exposition of the method of isomonodromy deformations itself, which is an analogue in the theory of nonlinear ordinary differential equations of the familiar inverse problem method. Bibliography: 23 titles.

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