On the Tritronquée Solutions of (Formula presented.)

Tamara Grava, Andrei Kapaev, Christian Klein*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)


For equation (Formula presented.), the second member in the PI hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $$t$$t and evaluate the asymptotics in the complex x plane for (Formula presented.) and t =o(x<sup>2/3</sup>). Using this result, we identify the most degenerate solutions (Formula presented.), called tritronquée; describe the quasi-linear Stokes phenomenon; and find the large $$n$$n asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronquée solutions.

Original languageEnglish
Pages (from-to)425-466
Number of pages42
JournalConstructive Approximation
Issue number3
Publication statusPublished - 18 Jun 2015


  • Numerical methods
  • Painlevé equations
  • Riemann–Hilbert problem
  • Tritronquée solutions


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