Journal of Mathematical Sciences

, Volume 73, Issue 4, pp 500–517 | Cite as

Essential singularity of the second-genus Painlevé function and the nonlinear stokes phenomenon

  • A. A. Kapaev
Article

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.

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Copyright information

© Plenum Publishing Corporation 1995

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  • A. A. Kapaev

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