Geodesic
The second Painlevé equation at a problem about nonlinear effects near caustics
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 110-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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An asymptotics at large time for nonlinear Schrödinger equation is studied in a critical case produced by some problems concerning nonlinear effects near caustics. The asymptotics is described in terms of the second Painlevé transcendent. 
@article{ZNSL_1991_187_a6,
     author = {B. I. Suleimanov},
     title = {The second {Painlev\'e} equation at a problem about nonlinear effects near caustics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--128},
     year = {1991},
     volume = {187},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a6/}
}
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B. I. Suleimanov. The second Painlevé equation at a problem about nonlinear effects near caustics. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 110-128. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a6/