On the algebraic solutions of the Painleve-III (D7) equation
Mathematical Physics
2022-09-28 v1 Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
The D7 degeneration of the Painleve-III equation has solutions that are rational functions of for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert representation of these solutions. We demonstrate the utility of this representation by analyzing rigorously the behavior of the solutions in the large parameter limit.
Keywords
Cite
@article{arxiv.2202.04217,
title = {On the algebraic solutions of the Painleve-III (D7) equation},
author = {Robert J. Buckingham and Peter D. Miller},
journal= {arXiv preprint arXiv:2202.04217},
year = {2022}
}
Comments
35 pages, 7 figures