Theoretical and Mathematical Physics

, Volume 137, Issue 2, pp 1515–1519 | Cite as

Tritronquée Solutions of Perturbed First Painlevé Equations

  • N. Joshi


We consider solutions of the class of ODEs y″ = 6y2 − xμ, which contains the first Painlevé equation (PI) for μ = 1. It is well known that PI has a unique real solution (called a tritronquée 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 μ ≠ 1.

Painlevé equations 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • N. Joshi
    • 1
  1. 1.School of Mathematics and Statistics F07University of SydneySydneyAustralia

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