Abstract
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 language | English |
---|---|
Pages (from-to) | 425-466 |
Number of pages | 42 |
Journal | Constructive Approximation |
Volume | 41 |
Issue number | 3 |
DOIs | |
Publication status | Published - 18 Jun 2015 |
Keywords
- Numerical methods
- Painlevé equations
- Riemann–Hilbert problem
- Tritronquée solutions