Geodesic
Scaling limits in the second Painlevé transcendent
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 60-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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By the isomonodromy deformation method, scaling limits in the second Painlevé equation $y_{xx}=2y^3+xy-\alpha$ depending on a complex parameter to and yielding formally equations for an elliptical sine and its degenerations are studied. Results contain the description of discriminant curves on the parameter $t_0$ plane, the proof of the solvability for the system of transcendent equations for an invariant $a_0(t_0)$ for the elliptical asymptotics of the Painlevé transcendent and the description of the main asymptotic terms of the second Painlevé transcendent as $\operatorname{Re}\alpha\to\infty$ for any to with the corresponding connection formulae together in the case of general position. Bibliography: 23 titles. 
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     author = {A. A. Kapaev},
     title = {Scaling limits in the second {Painlev\'e} transcendent},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--101},
     year = {1994},
     volume = {209},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a4/}
}
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A. A. Kapaev. Scaling limits in the second Painlevé transcendent. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 60-101. http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a4/