Special Solutions of the Sixth Painleve Equation with Solvable Monodromy

Details Special Solutions of the Sixth Painleve Equation with Solvable Monodromy Special Solutions of the Sixth Painleve Equation with Solvable Monodromy

2006-10-23

arxiv.org/abs/math/0610673v1

Mathematics

Classical Analysis and ODEs

15 pages, 6 figures

Scientific paper

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.

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