Elliptic asymptotics for the complete third Painlev\'e transcendents
Classical Analysis and ODEs
2025-02-18 v3
Abstract
For a general solution of the third Painlev\'e equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions. The expression is derived by using isomonodromy deformation of a linear system governed by the third Painlev\'e equation of this type. In our calculation of the WKB analysis, the treated Stokes curve ranges on both upper and lower sheets of the two sheeted Riemann surface.
Keywords
Cite
@article{arxiv.2211.00886,
title = {Elliptic asymptotics for the complete third Painlev\'e transcendents},
author = {Shun Shimomura},
journal= {arXiv preprint arXiv:2211.00886},
year = {2025}
}
Comments
37 pages. arXiv admin note: substantial text overlap with arXiv:2207.11495