Quasi-linear Stokes phenomenon for the Painleve first equation

Series: 
Analysis Seminar
Tuesday, April 7, 2009 - 16:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Indiana University-Purdue University Indianapolis
Solutions of the simplest of the Painleve equations, PI, y'' = 6y^2+x, exhibit surprisingly rich asymptotic properties as x is large. Using the Riemann-Hilbert problem approach, we find an exponentially small addition to an algebraically large background admitting a power series asymptotic expansion and explain how this "beyond of all orders" term helps us to compute the coefficient asymptotics in the preceding series.