| Abstract: | By the isomonodromic deformation method, the leading term of the elliptic asymptotics as x→∞ of the solution of the second
Painlevé equation is constructed in the generic case. The equations for the modulus of this elliptic sine (which depends only
on arg x) are given. The phase of the elliptic sine for any arg x is explicitly expressed in terms of first integrals of the
Painlevé equation, i.e., in terms of the Stokes multipliers of the associated linear system. A nonlinear Stokes phenomenon
typical for the asymptotic behavior of the Painlevé function is described. Bibliography: 25 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 187, pp. 139–170, 1990.
Translated by O. A. Ivanov. |
