Theoretical and Mathematical Physics

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

Tritronquée Solutions of Perturbed First Painlevé Equations

  • N. Joshi

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    P. Boutroux, Ann. École Normale Sup., 30, 265-375 (1913).Google Scholar
  2. 2.
    N. Joshi and A. V. Kitaev, Stud. Appl. Math, 107, 253-291 (2001).Google Scholar
  3. 3.
    N. Joshi and M. D. Kruskal, Stud. Appl. Math., 93, 187-207 (1994).Google Scholar
  4. 4.
    W. R. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Krieger, Huntington, NY (1976).Google Scholar
  5. 5.
    F. W. J. Olver, Asymptotics and Special Functions, Acad. Press, London (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

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

Personalised recommendations