This article is cited in 6 papers

Tritronquée Solutions of Perturbed First Painlevé Equations

N. Joshi

University of Sydney

Abstract: 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 $\mu\ne1$.

Keywords: Painlevé equations.

DOI: 10.4213/tmf263

 English version: Theoretical and Mathematical Physics, 2003, 137:2, 1515–1519

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