Geodesic
Tritronquée Solutions of Perturbed First Painlevé Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 188-192 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider solutions of the class of ODEs $y''=6y^2-x^{\mu}$, which contains the first Painlevé equation $($PI$)$ for $\mu=1$. It is well known that PI has a unique real solution (called a tritronquйe solution) asymptotic to $-\sqrt{x/6}$ and decaying monotonically on the positive real line. We prove the existence and uniqueness of a corresponding solution for each real nonnegative $\mu\ne1$.
Mots-clés : Painlevé equations. 
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     author = {N. Joshi},
     title = {Tritronqu\'ee {Solutions} of {Perturbed} {First} {Painlev\'e} {Equations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a3/}
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N. Joshi. Tritronquée Solutions of Perturbed First Painlevé Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 188-192. http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a3/

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