Claeys, Tom
[UCL]
We study the asymptotic behavior of a special smooth solution y(x, t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of the Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x, t) if x -> +/-infinity (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.
Bibliographic reference |
Claeys, Tom. Asymptotics for a special solution to the second member of the Painleve I hierarchy. In: Journal of physics a-mathematical and theoretical, Vol. 43, no. 43, p. - (2010) |
Permanent URL |
http://hdl.handle.net/2078.1/73373 |