Pole-free solutions of the first Painlev\'e hierarchy and non-generic critical behavior for the KdV equation
Mathematical Physics
2015-05-28 v1 Classical Analysis and ODEs
Complex Variables
math.MP
Abstract
We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of solutions to the KdV equation in the small dispersion limit. This was understood in the case of a generic critical point, and we generalize it here to the case of non-generic critical points.
Cite
@article{arxiv.1107.0214,
title = {Pole-free solutions of the first Painlev\'e hierarchy and non-generic critical behavior for the KdV equation},
author = {Tom Claeys},
journal= {arXiv preprint arXiv:1107.0214},
year = {2015}
}
Comments
29 pages