Asymptotics for a special solution to the second member of the Painleve I hierarchy

Details Asymptotics for a special solution to the second member of the Painleve I hierarchy Asymptotics for a special solution to the second member of the Painleve I hierarchy

2010-01-13

arxiv.org/abs/1001.2213v2

Physics

Mathematical Physics

19 pages

Scientific paper

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 Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x,t) if x\to \pm\infty (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.

Affiliated with

Also associated with

No associations

Rating

Asymptotics for a special solution to the second member of the Painleve I hierarchy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotics for a special solution to the second member of the Painleve I hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotics for a special solution to the second member of the Painleve I hierarchy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-525736