Largedegree asymptotics of rational PainlevéII functions: noncritical behaviour
Abstract
Rational solutions of the inhomogeneous PainlevéII equation and of a related coupled PainlevéII system have recently arisen in studies of fluid vortices and of the sineGordon equation. For the sineGordon application in particular it is of interest to understand the largedegree asymptotic behaviour of the rational PainlevéII functions. We explicitly compute the leadingorder largedegree asymptotics of these two families of rational functions valid in the whole complex plane with the exception of a neighbourhood of a certain piecewisesmooth closed curve. We obtain rigorous error bounds by using the DeiftZhou nonlinear steepestdescent method for RiemannHilbert problems.
 Publication:

Nonlinearity
 Pub Date:
 October 2014
 DOI:
 10.1088/09517715/27/10/2489
 Bibcode:
 2014Nonli..27.2489B