Trans-Series Asymptotics of Solutions to the Degenerate Painlev\'{e} III Equation: A Case Study
Classical Analysis and ODEs
2025-08-15 v7 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
A one-parameter family of trans-series asymptotics of solutions to the Degenerate Painlev\'{e} III Equation (DP3E) are parametrised in terms of the monodromy data of an associated two-by-two linear auxiliary problem via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the sigma-forms of the DP3E are also obtained. The actions of Lie-point symmetries for the DP3E are derived.
Keywords
Cite
@article{arxiv.2010.11235,
title = {Trans-Series Asymptotics of Solutions to the Degenerate Painlev\'{e} III Equation: A Case Study},
author = {A. Vartanian},
journal= {arXiv preprint arXiv:2010.11235},
year = {2025}
}