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The essential singularity of the second Painlevé function and the nonlinear Stokes phenomenon. (Russian. English summary) Zbl 0746.34006
Summary: On the base of the isomonodromy deformation method the elliptical asymptotics in complex domain of argument of Boutroux type for the second Painlevé function is constructed. The equations for the modul which depends only on $\arg x$ of elliptical sine are written down. The phase of elliptical sine for any $\arg x$ except the Stokes rays is expressed in terms of Stokes multipliers of the associated linear system. The last are the first integrals of Painlevé functions. The nonlinear Stokes phenomenon for the second Painlevé equation is described.

34M55Painlevé and other special equations; classification, hierarchies
34E05Asymptotic expansions (ODE)
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