English

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 x1/3x^{1/3} 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