Geodesic
Tronquée Solutions of the Third and Fourth Painlevé Equations
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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Recently in a paper by Lin, Dai and Tibboel, it was shown that the third and fourth Painlevé equations have tronquée and tritronquée solutions. We obtain global information about these tronquée and tritronquée solutions. We find their sectors of analyticity, their Borel summed representations in these sectors as well as the asymptotic position of the singularities near the boundaries of the analyticity sectors. We also correct slight errors in the paper mentioned.
Keywords: the third and fourth Painlevé equations; asymptotic position of singularities; tronquée solutions; tritronquée solutions; Borel summed representation. 
@article{SIGMA_2018_14_a94,
     author = {Xiaoyue Xia},
     title = {Tronqu\'ee {Solutions} of the {Third} and {Fourth} {Painlev\'e} {Equations}},
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     year = {2018},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a94/}
}
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Xiaoyue Xia. Tronquée Solutions of the Third and Fourth Painlevé Equations. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a94/

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