English

Special Solutions of the Sixth Painleve Equation with Solvable Monodromy

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We will study two types of special solutions of the sixth Painleve equation, which are invariant under the symmetries obtained from the Backlund transformations. In most cases, the fixed points of the Backlund transformations are classical solution, but our solutions are not classical for generic parameters. We will calculate the linear monodromy of these solutions exactly, and we will characterize them on Fricke's cubic surface of monodromy.

Keywords

Cite

@article{arxiv.math/0610673,
  title  = {Special Solutions of the Sixth Painleve Equation with Solvable Monodromy},
  author = {Kazuo Kaneko and Shoji Okumura},
  journal= {arXiv preprint arXiv:math/0610673},
  year   = {2007}
}

Comments

15 pages, 6 figures