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Zbl 0746.34006
Kapaev, A.A.
The essential singularity of the second Painlevé function and the nonlinear Stokes phenomenon. (Russian. English summary)
[J] Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 187, 139-170 (1991). ISSN 0373-2703

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.

MSC 2000:: *34M55 Painlevé and other special equations
34E05 Asymptotic expansions (ODE)

Keywords: isomonodromy deformation method; elliptical asymptotics; Boutroux type; second Painlevé function; elliptical sine; nonlinear Stokes phenomenon; second Painlevé equation

Cited in: Zbl 0834.34010

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