Asymptotics for a special solution to the second member of the Painleve I hierarchy
(2010) Journal of Physics A: Mathematical and Theoretical — Vol. 43, n° 43 (2010)
Files
No attached file found for this publication.
Details
- Authors
- Abstract
- 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.
- Affiliations
Citations
Claeys, T. (2010). Asymptotics for a special solution to the second member of the Painleve I hierarchy. Journal of Physics A: Mathematical and Theoretical, 43(43). https://doi.org/10.1088/1751-8113/43/43/434012 (Original work published 2010)